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BEGIN:VEVENT
SUMMARY:Marija Galic (Univerzity of Zagreb)
DTSTART;VALUE=DATE-TIME:20201006T070000Z
DTEND;VALUE=DATE-TIME:20201006T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/5
DESCRIPTION:Title: Existence of a weak solution to a 3d nonlinear\, moving boundary FSI pr
oblem\nby Marija Galic (Univerzity of Zagreb) as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\n\nAbstract\nWe consider a nonlinear\, moving boundary\, fluid-struc
ture interaction problem\nbetween an incompressible\, viscous fluid flow\,
and an elastic structure composed\nof a cylindrical shell supported by a
mesh-like elastic structure. The\nfluid flow is modeled by the time-depend
ent Navier-Stokes equations in a threedimensional\ncylindrical domain\, wh
ile the cylindrical shell is described by the\ntwo-dimensional linearly el
astic Koiter shell equations allowing displacements\nin all three spatial
directions. The mesh-like structure is modeled as a onedimensional\nhyperb
olic net made of linearly elastic curved rods. The fluid and\nthe mesh-sup
ported structure are coupled via the kinematic and dynamic boundary\ncoupl
ing conditions describing continuity of velocity and balance of contact\nf
orces at the fluid-structure interface. We prove the existence of a weak s
olution\nto this nonlinear\, moving boundary problem by using the time-dis
cretization\nvia Lie operator splitting method\, Arbitrary Lagrangian-Eule
rian mapping and\nnon-trivial compactness result. This is a joint work wit
h Suncica Canic and \nBoris Muha.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralph Chill (Technical University of Dresden)
DTSTART;VALUE=DATE-TIME:20201013T065000Z
DTEND;VALUE=DATE-TIME:20201013T082000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/6
DESCRIPTION:Title: Degenerate gradient systems: the bidomain problem and Dirichlet-to-Neum
ann operators\nby Ralph Chill (Technical University of Dresden) as par
t of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathema
tics\,Zitna 25\,Prague.\n\nAbstract\nWe identify a common structure behind
several parabolic PDE\nmodels involving\nDirichlet-to-Neumann operators\,
the bidomain operator\, and some more\,\nand we show that\nthey actually
have a gradient structure\, possibly up to lower order\nperturbations. Thi
s has\nconsequences for wellposedness of these PDEs\, regularity of soluti
ons\nand their asymptotic\nbehaviour.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Sperone (Faculty of Mathematics and Physics\, Charles Un
iversity in Prague)
DTSTART;VALUE=DATE-TIME:20201020T065000Z
DTEND;VALUE=DATE-TIME:20201020T082000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/7
DESCRIPTION:Title: Explicit bounds for the generation of a lift force exerted by steady-st
ate Navier-Stokes flows over a fixed obstacle\nby Gianmarco Sperone (F
aculty of Mathematics and Physics\, Charles University in Prague) as part
of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathemati
cs\,Zitna 25\,Prague.\n\nAbstract\nWe analyze the steady motion of a visco
us incompressible fluid\nin a two- and three-dimensional channel containin
g an obstacle through\nthe Navier-Stokes equations under different types o
f boundary\nconditions. In the 2D case we take constant non-homogeneous Di
richlet\nboundary data in a (virtual) square containing the obstacle\, and
\nemphasize the connection between the appearance of lift and the unique\n
solvability of Navier-Stokes equations. In the 3D case we consider mixed\n
boundary conditions: the inflow is given by a fairly general datum and\nth
e flow is assumed to satisfy a constant traction boundary condition on\nth
e outlet. In the absence of external forcing\, explicit bounds on the\ninf
low velocity guaranteeing existence and uniqueness of such steady\nmotion
are provided after estimating some Sobolev embedding constants\nand constr
ucting a suitable solenoidal extension of the inlet velocity.\nIn the 3D c
ase\, this solenoidal extension is built through the Bogovskii\noperator a
nd explicit bounds on its Dirichlet norm (in terms of the\ngeometric param
eters of the obstacle) are found by solving a variational\nproblem involvi
ng the infinity-Laplacian.\nThe talk accounts for results obtained in coll
aboration with Filippo\nGazzola and Ilaria Fragalà (both at Politecnico d
i Milano).\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Piasecki (Univerzity of Warsaw)
DTSTART;VALUE=DATE-TIME:20201103T075000Z
DTEND;VALUE=DATE-TIME:20201103T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/8
DESCRIPTION:Title: A maximal regularity approach to compressible mixtures\nby Tomasz P
iasecki (Univerzity of Warsaw) as part of Necas PDE seminar\n\nLecture hel
d in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\n
I will present recent results obtained in collaboration with Yoshihiro\nSh
ibata and Ewelina Zatorska. We investigate the well posedness of a\nsystem
describing flow of a mixture of compressible constituents.\nThe system in
composed of Navier-Stokes equations coupled with equations\ndescribing ba
lance of fractional masses. A crucial property is that the\nsystem is non-
symmetric and only degenerate parabolic.\nHowever\, it reveals a structure
which allows to transform it to a\nsymmetric parabolic problem using appr
opriate change of unknowns. In order\nto treat the transformed problem we
write it in Lagrangian coordinates and\nlinearize.\nFor the related linear
problem we show a Lp-Lq maximal regularity estimate\napplying the theory
of R-bounded solution operators. This estimate allows\nto show local exist
ence and uniqueness. Next\, assuming additionally\nboundedness of the doma
in we extend the maximal regularity estimate and\nshow exponential decay
property for the linear problem. This allow us to\nshow global well-posedn
ess of the original problem for small data.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Bravin (Basque Center for Applied Mathematics)
DTSTART;VALUE=DATE-TIME:20201124T075000Z
DTEND;VALUE=DATE-TIME:20201124T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/9
DESCRIPTION:Title: Interaction of a small rigid body with fluids\nby Marco Bravin (Bas
que Center for Applied Mathematics) as part of Necas PDE seminar\n\nLectu
re held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbst
ract\nIn this talk I will present a recent result in collaboration with Pr
of Necasova\, where we study the interaction between a small rigid body an
d a compressible viscous fluid modeled by the compressible Navier-Stokes e
quations.\n\nIn particular I will recall the previous results where the fl
uids were supposedly incompressible and then I will focus my attention on
the improved pressure estimates that are the main novelty in our result. I
n contrast with the incompressible case the pressure estimates depend on a
lower bound of the mass and the inertia matrix of the object as its size
tends to zero.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalousek (Institute of Mathematics\,CAS)
DTSTART;VALUE=DATE-TIME:20201201T075000Z
DTEND;VALUE=DATE-TIME:20201201T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/10
DESCRIPTION:Title: Global existence of weak solutions for a magnetic fluid model\nby
Martin Kalousek (Institute of Mathematics\,CAS) as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nThe talk is devoted to the presentation of recent results
that concern the global in time existence of weak solutions of a system o
f partial differential equations modeling a diffuse interface flow of two
Newtonian incompressible magnetic fluids. The system consists of the incom
pressible Navier-Stokes equations coupled with an evolutionary equation fo
r the magnetization vector and the Cahn-Hilliard equations. Presented resu
lts are based on the joint work with S. Mitra and A. Schlömerkemper.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tong Tang (University of Nanjing)
DTSTART;VALUE=DATE-TIME:20201208T075000Z
DTEND;VALUE=DATE-TIME:20201208T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/11
DESCRIPTION:Title: Global existence of weak solutions to the quantum Navier-Stokes equati
ons\nby Tong Tang (University of Nanjing) as part of Necas PDE seminar
\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague
.\n\nAbstract\nIn this talk\, we proved the global existence of weak solut
ions to the\nquantum Navier-Stokes equations with non-monotone pressure. M
otivated by\nthe work of Antonell-Spirito(2017\, Arch. Ration. Mech. Anal.
\, 1161-1199)\nand Ducomet-Necasova-Vasseur (2010\, Z. Angew. Math. Phys.\
, 479-491)\, we\nconstruct the suitable approximate system and obtain the
corresponding\ncompactness by B-D entropy estimate and Mellet-Vasseur ineq
uality.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Danchin (University of Creteil)
DTSTART;VALUE=DATE-TIME:20201215T075000Z
DTEND;VALUE=DATE-TIME:20201215T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/12
DESCRIPTION:Title: A class of global relatively smooth solutions for the Euler-Poisson sy
stem\nby Raphael Danchin (University of Creteil) as part of Necas PDE
seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\
,Prague.\n\nAbstract\nIn this joint work with X. Blanc\, B. Ducomet and Š
.\nNečasová (to appear in JHDE)\, we construct a class of global solutio
ns\nto the Cauchy problem for the isentropic Euler equations coupled with\
nthe Poisson equation\, in the whole space. The initial density is assumed
\nto decay to 0 at infinity and the initial velocity is close to some\nref
erence velocity with Jacobian having positive spectrum bounded away\nfrom
0. By a suitable adaptation of Grassin-Serre’s work on the\n`pure’ com
pressible Euler equations\, we obtain a global smooth\nsolution the large
time behavior of which may be described in terms of\nsome solution of the
multi-dimensional Burgers equation. The stability\nof some special spheri
cally symmetric stationary solution is also\ndiscussed.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Mucha (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20210105T075000Z
DTEND;VALUE=DATE-TIME:20210105T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/13
DESCRIPTION:Title: Flows initiated by ripped densities\nby Piotr Mucha (University of
Warsaw) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Insti
tute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe address the questio
n: Are solutions to the equations of\nviscous flows that are initiated by
a density function given by a\ncharacteristic function of a set regular an
d unique? The positive\nanswer is possible for the compressible Navier-St
okes equations if the\nbulk/volume viscosity is large. The limit case of t
he homogeneous\nincompressible NSEs will be discussed too.\nThe talk will
be based on results with Raphael Danchin:\nRD\, PBM: Compressible NSEs wit
h ripped density\, arXiv\;\nRD\, PBM: The incompressible NSEs in vacuum\,
CPAM2019.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART;VALUE=DATE-TIME:20210126T075000Z
DTEND;VALUE=DATE-TIME:20210126T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/14
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART;VALUE=DATE-TIME:20210202T075000Z
DTEND;VALUE=DATE-TIME:20210202T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/15
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART;VALUE=DATE-TIME:20210209T075000Z
DTEND;VALUE=DATE-TIME:20210209T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/16
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART;VALUE=DATE-TIME:20210216T075000Z
DTEND;VALUE=DATE-TIME:20210216T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/17
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:semester break
DTSTART;VALUE=DATE-TIME:20210223T075000Z
DTEND;VALUE=DATE-TIME:20210223T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/18
DESCRIPTION:by semester break as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Coti Zelati (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210316T080000Z
DTEND;VALUE=DATE-TIME:20210316T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/19
DESCRIPTION:Title: Stationary Euler flows near the Kolmogorov and Poiseuille flows\nb
y Michele Coti Zelati (Imperial College London) as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nWe exhibit a large family of new\, non-trivial stationary
\nstates of\nanalytic regularity\, that are arbitrarily close to the Kolmo
gorov flow\non the\nsquare torus. Our construction of these stationary sta
tes builds on a\ndegeneracy in the global structure of the Kolmogorov flow
. This is in\ncontrast\nwith both the Kolmogorov flow on a rectangular tor
us and the\nPoiseuille flow\nin a channel\, for which we can show that the
only stationary states\nnear them\nmust be shears. This has surprising co
nsequences in the context of\ninviscid\ndamping in 2D Euler and enhanced d
issipation in Navier-Stokes.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Hofmanova (University of Bielefeld)
DTSTART;VALUE=DATE-TIME:20210406T070000Z
DTEND;VALUE=DATE-TIME:20210406T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/20
DESCRIPTION:Title: Non-uniqueness in law of stochastic 3D Navier--Stokes equations\nb
y Martina Hofmanova (University of Bielefeld) as part of Necas PDE seminar
\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague
.\n\nAbstract\nWe consider the stochastic Navier--Stokes equations in thr
ee dimensions and prove that the law of analytically weak solutions is not
unique. In particular\, we focus on two iconic examples of a stochastic p
erturbation: either an additive or a linear multiplicative noise driven by
a Wiener process. In both cases\, we develop a stochastic counterpart of
the convex integration method introduced recently by Buckmaster and Vicol
. This permits to construct probabilistically strong and analytically weak
solutions defined up to a suitable stopping time. In addition\, these sol
utions fail the corresponding energy inequality at a prescribed time with
a prescribed probability. Then we introduce a general probabilistic constr
uction used to extend the convex integration solutions beyond the stopping
time and in particular to the whole time interval $[0\,\\infty)$. Finally
\, we show that their law is distinct from the law of solutions obtained b
y Galerkin approximation. In particular\, non-uniqueness in law holds on a
n arbitrary time interval $[0\,T]$\, $T>0$.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fanelli (University of Lyon)
DTSTART;VALUE=DATE-TIME:20210413T070000Z
DTEND;VALUE=DATE-TIME:20210413T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/21
DESCRIPTION:Title: Statistical solutions to the barotropic Navier-Stokes equations\nb
y Francesco Fanelli (University of Lyon) as part of Necas PDE seminar\n\nL
ecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\n
Abstract\nIn this talk we are concerned with the notion of statistical sol
utions to some models of fluid mechanics. We focus on the barotropic Navie
r-Stokes equations\, supplemented with non-homogeneous boundary data.\nIn
the first part of the talk\, we study dynamical properties of statistical
solutions. Our approach\, different from the classical one of Foiaş-Prodi
and Vishik-Fursikov for the incompressible system\, is based on a semiflo
w selection procedure. This allows us to define statistical solution as th
e push-forward measure of the initial probability distribution on the spac
e of data of the Navier-Stokes system. We then investigate questions like
existence and stability of statistical solutions.\nIn the second part of t
he talk\, we focus on the special class of stationary statistical solution
s. In particular\, we explore their role in the investigation of the valid
ity of the so-called ergodic hypothesis in the context of the barotropic N
avier-Stokes equations.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lannes (University of Bordeaux)
DTSTART;VALUE=DATE-TIME:20210302T080000Z
DTEND;VALUE=DATE-TIME:20210302T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/22
DESCRIPTION:Title: Some problems arising in wave-structure interactions\nby David Lan
nes (University of Bordeaux) as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nTh
ere are different formulations of the water waves problem. One of\nthem is
to formulate it as a system of equations coupling two\nquantities\, e.g.
the free surface elevation $\\zeta$ and the horizontal\ndischarge $Q$. Act
ually\, one can understand the water waves problem as\na system on three q
uantities\, $\\zeta$\, $Q$ and the surface pressure\n$P_s$ under the const
raint that $P_s$ is constant (and therefore\ndisappears from the equations
).\nWhen we consider in addition a floating body then\, under the body\, w
e\nstill have a system of equations on the same three quantities\, but\nth
is time the constraint is not on the pressure but on the surface of\nthe w
ater\, that must coincide with the bottom of the floating object.\nWave-st
ructure interactions can be understood as the coupling of these\ntwo diffe
rent constrained problems. We shall briefly analyse this\ncoupling and sho
w among other things how it dictates the evolution of\nthe contact line be
tween the surface of the water and the surface of\nthe floating body\, and
how to transform it into transmission problems\nthat raise many mathemati
cal issues such as fully nonlineary\nhyperbolic initial boundary value pro
blems\, dispersive boundary\nlayers\, initial boundary value problems for
nonlocal equations\, etc.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vaclav Macha (Institute of Mathematics\, Czech Academy of Sciences
)
DTSTART;VALUE=DATE-TIME:20210309T080000Z
DTEND;VALUE=DATE-TIME:20210309T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/23
DESCRIPTION:Title: Local-in-time existence of strong solutions to a class of compressible
non-Newtonian Navier-Stokes equations\nby Vaclav Macha (Institute of
Mathematics\, Czech Academy of Sciences) as part of Necas PDE seminar\n\nL
ecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\n
Abstract\nWe show a local-in-time existence of a strong solution to the ge
neralized compressible Navier-Stokes equation for arbitrarily large initia
l data. The goal is reached by $L^p$-theory for linearized equations which
are obtained with help of the Weis multiplier theorem. This work was done
in collaboration with M. Kalousek and Š. Nečasová.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonin Novotny (University of Toulon)
DTSTART;VALUE=DATE-TIME:20210323T073000Z
DTEND;VALUE=DATE-TIME:20210323T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/24
DESCRIPTION:Title: Compressible fluids with nonhomogeneous boundary data I\nby Antoni
n Novotny (University of Toulon) as part of Necas PDE seminar\n\nLecture h
eld in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract
\nWe shall discuss several problems in the mathematical analysis of visco
us compressible\nfluids under the action of non zero inflow-outflow bounda
ry conditions.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonin Novotny (University of Toulon)
DTSTART;VALUE=DATE-TIME:20210330T070000Z
DTEND;VALUE=DATE-TIME:20210330T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/25
DESCRIPTION:Title: Compressible fluids with nonhomogeneous boundary data II\nby Anton
in Novotny (University of Toulon) as part of Necas PDE seminar\n\nLecture
held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstrac
t\nWe shall discuss several problems in the mathematical analysis of visc
ous compressible\nfluids under the action of non zero inflow-outflow bound
ary conditions.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART;VALUE=DATE-TIME:20210511T070000Z
DTEND;VALUE=DATE-TIME:20210511T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/26
DESCRIPTION:Title: R-solver\, Maximal Regularity and Mathematical Fluid Dynamics\nby
Yoshihiro Shibata (Waseda University) as part of Necas PDE seminar\n\nLect
ure held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbs
tract\nMaximal Regularity is an important tool to show the existence of st
rong solutions of quasi-linear system of parabolic equations\, for example
free boundary problems for the Navier-Stokes equations. In this lecture\,
I will talk about a systematic approach for the Lp maximal regularity by
using the R-solver. This approach is quite useful to control the high freq
uency part of solutions to the linearized problem\, and so we can prove th
e local well-posedness for the dynamical equations appearing in the mathem
atical fluid dynamics. But\, to prove the global well-posedness at least f
or small initial data\, we have to control the low frequency part. To do t
his I use so called Lp-Lq decay estimate for the semigroup group associate
d with the linearized problem\, like Stokes equations. In this talk\, I wi
ll present how to prove the maximal regularity by using an R-solver and ho
w to control the low frequency part by using Lp-Lq estimates to prove the
global wellposedness in some concrete example\, like equations describing
the compressible viscous fluid flow.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franc Merle (Université de Cergy-Pontoise)
DTSTART;VALUE=DATE-TIME:20210518T070000Z
DTEND;VALUE=DATE-TIME:20210518T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/27
DESCRIPTION:Title: On the implosion of a three dimensional compressible fluid\nby Fra
nc Merle (Université de Cergy-Pontoise) as part of Necas PDE seminar\n\nL
ecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\n
Abstract\nWe\nconsider the compressible three dimensional Navier Stokes an
d Euler\nequations. In a suitable regime of barotropic laws\, we construct
a set\nof finite energy smooth initial data for which the corresponding\n
solutions to both equations implode (with infinite density) at a later\nti
me at a point\, and completely describe the associated formation of\nsingu
larity. Two essential steps of analysis are the existence of very\nregular
self-similar solutions to the\ncompressible Euler equations for quantized
values of the speed and the\nderivation of spectral gap estimates for the
associated linearized flow\nwhich are addressed in the companion papers \
\cite{MRRSprofile\,\nMRRSdefoc}. All blow up dynamics obtained for the Nav
ier-Stokes problem\nare of type II (non self-similar).\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ewelina Zatorska (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210525T080000Z
DTEND;VALUE=DATE-TIME:20210525T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/28
DESCRIPTION:Title: Low Mach and low Froude numbers limit for the compressible Navier-Stok
es equations with density-dependent viscosity coefficients\nby Ewelina
Zatorska (Imperial College London) as part of Necas PDE seminar\n\nLectur
e held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstr
act\nIn this talk I will present a recent result on singular limit for com
pressible Navier-Stokes equations involving low Mach and low Froude number
s. We assume that the physical domain is the periodic box in three space d
imensions\, and that the limiting density profile is smooth\, separated fr
om zero and bounded from above. Derivation of the\, so-called\, anelastic
approximation was proven previously by N. Masmoudi in 2007\, who used as a
n approximation the barotropic compressible Navier-Stokes equations with c
onstant viscosity coefficients. In our result\, the approximate system inc
ludes the viscosity coefficients depending on the density and the singular
form of the pressure.\nThe result is based on a joint paper with Francesc
o Fanelli.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Maremonti (Università della Campania Luigi Vanvitelli)
DTSTART;VALUE=DATE-TIME:20210504T070000Z
DTEND;VALUE=DATE-TIME:20210504T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/29
DESCRIPTION:Title: On the uniqueness of a suitable weak solution to the Navier-Stokes Cau
chy problem\nby Paolo Maremonti (Università della Campania Luigi Vanv
itelli) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Instit
ute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe are dealing with the
Navier-Stokes Cauchy problem. We investigate some results of regularity a
nd uniqueness related to suitable weak\nsolutions. The suitable weak solut
ion notion is meant in the sense introduced by Caffarelli-Kohn-Nirenberg.
In paper [1]\, we recognize that a\nsuitable weak solution enjoys more reg
ularity than Leray-Hopf weak solutions\, that allows us to furnish new uni
queness results for the solutions.\nActually\, we realize two results. The
first one is a new sufficient condition on the initial datum u0 for uniqu
eness. We work on existing suitable\nweak solution\, that is\, we do not c
onstruct a more regular weak solution\ncorresponding to our initial datum.
The second result employs a weaker\ncondition with respect to previous on
es (almost $u_0 \\in L^2$)\, but\, just for\none of the two compared weak
solutions\, we need a “special” Prodi-Serrin\ncondition. It is “spe
cial” as it is local in space.\n\nReferences: [1] Crispo F. and Maremont
i P.\, On the uniqueness of a suitable weak solution\nto the Navier-Stokes
Cauchy problem\, SN Partial Differential Equations and\nApplications\, to
appear.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Flandoli (University of Pisa)
DTSTART;VALUE=DATE-TIME:20210427T070000Z
DTEND;VALUE=DATE-TIME:20210427T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/30
DESCRIPTION:Title: Mixing and dissipation properties of transport noise\nby Franco Fl
andoli (University of Pisa) as part of Necas PDE seminar\n\nLecture held i
n Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThi
s talk is based on recent works with Dejun Luo and Lucio\nGaleati devoted
to the investigation of a suitable scaling limit of\nseveral different PDE
models subject to transport noise\, when the noise\nis extremized in a su
itable limit sense. Among the consequences there\nare certain forms of mix
ing\, enhanced dissipation\, delayed blow-up due\nto noise\; these results
hold for several classes of equations including\nEuler and Navier-Stokes
equations\, Keller-Siegel and reaction diffusion\nequations\; and also rig
orous results on eddy viscosity and eddy\ndissipation in turbulent fluids
have been proved. Along with arguments\nof stochastic model reduction\, de
veloped with Umberto Pappalettera\, a\npicture arises of the potential eff
ects of small scale fluctuations on\nlarge scale properties of turbulent f
luids.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mythily Ramaswamy (ICTS-TIFR\,India)
DTSTART;VALUE=DATE-TIME:20210420T070000Z
DTEND;VALUE=DATE-TIME:20210420T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/31
DESCRIPTION:Title: Local stabilization of time periodic flows\nby Mythily Ramaswamy (
ICTS-TIFR\,India) as part of Necas PDE seminar\n\nLecture held in Blue Hal
l\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nFluid flows h
ave been studied for a long time\, with a view to\nunderstand better the
models like channel flow\, blood flow\, air flow in the lungs\netc.\nHere
we focus on time periodic fluid flow models.\nLocal stabilization here co
ncerns the decay of the perturbation in the\nflow near a periodic trajecto
ry.\nThe main motivating example\nis the incompressible Navier-Stokes syst
em.\nI will discuss the general framework to study periodic solutions\nand
then indicate some results in this direction.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nilasis Chaudhuri (TU Berlin)
DTSTART;VALUE=DATE-TIME:20210615T070000Z
DTEND;VALUE=DATE-TIME:20210615T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/32
DESCRIPTION:Title: Convergence of consistent approximations to the complete compressible
Euler system\nby Nilasis Chaudhuri (TU Berlin) as part of Necas PDE se
minar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,P
rague.\n\nAbstract\nThe aim of the talk is to discuss a result on the weak
limit of\na `consistent approximation scheme' to the compressible complet
e Euler\nsystem in the full space $ \\mathbb{R}^d\,\\\; d=2\,3 $. The main
result states\nthat if a weak limit of the consistent approximation schem
e is a weak\nsolution of the system\, then the approximate solutions conve
rge locally\nstrongly (or at least almost everywhere) in suitable norms un
der a minimal\nassumption on the initial data of the approximate solutions
. The class of\nconsistent approximate solutions is quite general and incl
udes the\nvanishing viscosity and heat conductivity limit. In particular\,
they do\nnot have to satisfy the minimal principle for entropy.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Oschmann/Peter Bella (University of Dortmund)
DTSTART;VALUE=DATE-TIME:20210908T070000Z
DTEND;VALUE=DATE-TIME:20210908T100000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/33
DESCRIPTION:Title: Inverse of divergence and homogenization of compressible Navier-Stokes
equations in randomly perforated domains/Regularity for degenerate ellipt
ic equations\nby Florian Oschmann/Peter Bella (University of Dortmund)
as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of
Mathematics\,Zitna 25\,Prague.\n\nAbstract\nFlorian Oschmann\n\nInverse of
divergence and homogenization of compressible Navier-Stokes equations in
randomly perforated domains\n\nIn homogenization of compressible Navier-St
okes equations\, an inverse of the divergence operator (called Bogivski\\u
{\\i} operator) is crucial to obtain a-priori bounds for the velocity and
density independent of the perforation. Such Bogovski\\u{\\i} operators an
d bounds are well known in the case of periodically arranged holes with fi
xed diameter\, where the mutual distance is of order $\\varepsilon>0$ and
the radii scale like $\\varepsilon^\\alpha$ for some $\\alpha>3$. We gener
alize these results to the case of randomly distributed holes with random
radii and give applications to the homogenization of the Navier-Stokes(-Fo
urier) equations in such randomly perforated domains.\n\nPeter Bella\n\nI
discuss local regularity properties of solutions of linear\nnon-uniformly
elliptic equations with non-constant coefficients. Assuming certain integr
ability conditions on the ellipticity of the coefficient field\, we obtain
local boundedness of weak solutions and corresponding Harnack inequality.
The assumed integrability assumptions are sharp and improve upon classica
l results in the literature (Trudinger). I will also discuss analogous res
ult for the time-independent parabolic equations as well as application to
study of the variational integrals with differential (p\,q) growth.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milan Pokorny (Charles University)
DTSTART;VALUE=DATE-TIME:20211005T070000Z
DTEND;VALUE=DATE-TIME:20211005T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/34
DESCRIPTION:Title: Steady compressible Navier-Stokes-Fourier system with Dirichlet bounda
ry conditions for the temperature\nby Milan Pokorny (Charles Universit
y) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute o
f Mathematics\,Zitna 25\,Prague.\n\nAbstract\nBased on recent result by Ch
audhuri and Feireisl for the evolutionary NSF system we present the proof
of existence of weak (and variational entropy) solutions to the steady ver
sion with Dirichlet boundary conditions for the temperature. The formulati
on is based\, similarly as in the evolutionary case\, on a version of ball
istic energy inequality which allows to obtain a priori estimates for the
temperature and velocity.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil Skrizkovsky (Charles University)
DTSTART;VALUE=DATE-TIME:20211019T070000Z
DTEND;VALUE=DATE-TIME:20211019T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/35
DESCRIPTION:Title: Evolutionary compressible Navier-Stokes-Fourier system in two space di
mensions with adiabatic exponent almost one\nby Emil Skrizkovsky (Char
les University) as part of Necas PDE seminar\n\nLecture held in Blue Hall\
, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nIn this talk we
consider the full Navier-Stokes-Fourier system and\npresent the proof of
the existence of a weak solution in two space\ndimensions for the pressure
law given by $p(\\varrho\,\\theta) \\sim\n\\varrho\\theta + \\varrho \\lo
g^\\alpha(1+\\varrho)+ \\theta^4$\, which can be\nviewed as a close approx
imation of the pressure law for ideal gas\n$p(\\varrho\,\\theta) \\sim \\v
arrho\\theta$. The weak solutions with entropy\ninequality and total energ
y balance are considered and the existence of\nthis type of weak solutions
without any restriction on the size of the\ninitial conditions or the rig
ht-hand sides is shown provided $\\alpha >\n\\frac{17+\\sqrt{417}}{16}\\co
ng 2.34$.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danica Basaric (Institute of Mathematics\,CAS)
DTSTART;VALUE=DATE-TIME:20211026T070000Z
DTEND;VALUE=DATE-TIME:20211026T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/36
DESCRIPTION:Title: Existence of weak solutions for models of general compressible viscous
fluids with linear pressure\nby Danica Basaric (Institute of Mathemat
ics\,CAS) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Inst
itute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nIn this talk we will
focus on the existence of weak solutions for a system describing a general
compressible viscous fluid in the case of the pressure being a linear fun
ction of the density and the viscous stress tensor being a non-linear func
tion of the symmetric velocity gradient. More precisely\, we will first pr
ove the existence of dissipative solutions and study under which condition
s it is possible to guarantee the existence of weak solutions\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Radosevic (University of Zagreb)
DTSTART;VALUE=DATE-TIME:20211102T080000Z
DTEND;VALUE=DATE-TIME:20211102T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/37
DESCRIPTION:Title: On the regularity of weak solutions to the fluid-rigid body interactio
n problem\nby Ana Radosevic (University of Zagreb) as part of Necas PD
E seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 2
5\,Prague.\n\nAbstract\nThe fluid-structure interaction (FSI) systems are
multi-physics systems that\ninclude a fluid and solid component. They are
everyday phenomena with a wide\nrange of applications. The simplest model
for the structure is a rigid body. We\nstudy a nonlinear moving boundary f
luid-structure interaction problem where the\nfluid flow is governed by 3D
Navier-Stokes equations\, and the structure is a rigid\nbody described by
a system of ordinary differential equations called Euler equations\nfor t
he rigid body. Our goal is to show that a weak solution that additionally\
nsatisfy Prodi-Serrin condition is smooth on the interval of its existence
\, which is a\ngeneralization of the well-known regularity result for the
Navier-Stokes equations.\nThis is a joint work with Boris Muha and Sarka N
ecasova.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Srdjan Trifunovic (University of Novi Sad)
DTSTART;VALUE=DATE-TIME:20211109T080000Z
DTEND;VALUE=DATE-TIME:20211109T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/38
DESCRIPTION:Title: On the fluid-structure interaction problem with heat exchange\nby
Srdjan Trifunovic (University of Novi Sad) as part of Necas PDE seminar\n\
nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n
\nAbstract\nHere\, I will talk about a nonlinear interaction problem betwe
en a thermoelastic\nshell and a heat-conducting fluid. The shell is govern
ed by linear thermoelasticity\nequations and constitutes a time-dependent
domain which is filled with a fluid\ngoverned by the full Navier-Stokes-Fo
urier system. The fluid and the shell are fully\ncoupled\, giving rise to
a new previously unstudied interaction problem involving\nheat exchange. T
he existence of a weak solution for this problem is obtained by\ncombining
three approximation techniques - decoupling\, penalization and domain\nex
tension for fluid.\nThis talk is based on a joint work with Václav Mácha
\, Boris Muha\, Šárka\nNečasová and Arnab Roy.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Mitra (University of Wuerzburg)
DTSTART;VALUE=DATE-TIME:20211116T080000Z
DTEND;VALUE=DATE-TIME:20211116T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/39
DESCRIPTION:Title: A control problem of a linear compressible fluid-structure interactio
n model.\nby Sourav Mitra (University of Wuerzburg) as part of Necas P
DE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\n\nAbstract\nI will talk about a result on the controllability
of a compressible FSI model where the structure is located at a part of
the fluid boundary. I will first introduce the notion of control and exp
lain the tools to prove the controllability of a linear PDE. In the next
part of the talk I will introduce the FSI model under consideration and c
orresponding linearization. Finally I will speak about the control of the
linearized FSI problem and outline a proof.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patricia Clara (Politechnico di Milano)
DTSTART;VALUE=DATE-TIME:20211123T080000Z
DTEND;VALUE=DATE-TIME:20211123T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/40
DESCRIPTION:Title: Existence and uniqueness result for a fluid-structure-interaction evol
ution problem in an unbounded 2D channel\nby Patricia Clara (Politechn
ico di Milano) as part of Necas PDE seminar\n\nLecture held in Blue Hall\,
Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nIn an unbounded
2D channel\, we consider the vertical\ndisplacement of a rectangular obsta
cle in a regime of small flux for the\nincoming flow field\, modelling the
interaction between the cross-section\nof the deck of a suspension bridge
and the wind. We prove an existence\nand uniqueness result for a fluid-st
ructure-interaction evolution\nproblem set in this channel\, where at infi
nity the velocity field of the\nfluid has a Poiseuille flow profile. We in
troduce a suitable definition\nof weak solutions and we make use of a pena
lty method. In order to\nprevent the obstacle from going excessively far f
rom the equilibrium\nposition and colliding with the boundary of the chann
el\, we introduce a\nstrong force in the differential equation governing t
he motion of the\nrigid body and we find a unique global-in-time solution.
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongo Chae (Soeul University)
DTSTART;VALUE=DATE-TIME:20211214T080000Z
DTEND;VALUE=DATE-TIME:20211214T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/41
DESCRIPTION:Title: canceled\nby Dongo Chae (Soeul University) as part of Necas PDE se
minar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,P
rague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maja Szlenk (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20211130T080000Z
DTEND;VALUE=DATE-TIME:20211130T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/42
DESCRIPTION:Title: Uniqueness of weak solutions for the Stokes system for compressible fl
uids with general pressure\nby Maja Szlenk (University of Warsaw) as p
art of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathe
matics\,Zitna 25\,Prague.\n\nAbstract\nWe prove existence and uniqueness o
f global in time weak solutions for the Stokes system for compressible flu
ids with a general\, non-monotone pressure. We construct the solution at t
he level of Lagrangian formulation and then define the transformation to t
he original Eulerian coordinates. For a nonnegative and bounded initial de
nsity\, the solution is nonnegative for all $t>0$ as well and belongs to $
L^\\infty([0\,\\infty)\\times\\mathbb{T}^d)$. A key point of our considera
tions is the uniqueness of such transformation. Since the velocity might n
ot be Lipschitz continuous\, we develop a method which relies on the resul
ts of Crippa \\& De Lellis\, concerning regular Lagriangian flows. The uni
queness is obtained thanks to the application of a certain weighted flow a
nd detail analysis based on the properties of the $BMO$ space.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong Lu (Nanjing University)
DTSTART;VALUE=DATE-TIME:20220104T080000Z
DTEND;VALUE=DATE-TIME:20220104T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/43
DESCRIPTION:Title: Global solutions of 2D isentropic compressible Navier-Stokes equations
with one slow variable\nby Yong Lu (Nanjing University) as part of Ne
cas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Z
itna 25\,Prague.\n\nAbstract\nWe prove the global existence of solutions t
o the two-dimensional isentropic compressible Navier-Stokes equations with
smooth initial data which is slowly varying in one direction and with ini
tial density being away from vacuum. In particular\, we present examples o
f initial data which generate unique global smooth solutions to 2D compre
ssible Navier-Stokes equations with constant viscosity and with initial da
ta which are neither small perturbation of constant state nor of small ene
rgy.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Baptiste Clément (Czech Technical University)
DTSTART;VALUE=DATE-TIME:20220301T080000Z
DTEND;VALUE=DATE-TIME:20220301T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/45
DESCRIPTION:Title: Adaptive solution strategy for Richards' equation based on Discontinuo
us Galerkin methods and mesh refinement\nby Jean-Baptiste Clément (Cz
ech Technical University) as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nRicha
rds' equation describes flows in variably saturated\nporous media. Its sol
ution is challenging since it is a parabolic\nequation with nonlinearities
and degeneracies. In particular\, many\nreal-life problems are demanding
because they can involve\nsteep/heterogeneous hydraulics properties\, dyna
mic boundary conditions\nor moving sharp wetting fronts. In this regard\,
the aim is to design a\nrobust and efficient numerical method to solve Ric
hards’ equation.\nTowards this direction\, the work presented here deals
with\nDiscontinuous Galerkin methods which are very flexible discretizati
on\nschemes. They are combined with BDF methods to get high-order\nsolutio
ns. Built upon these desirable features\, an adaptive mesh\nrefinement str
ategy is proposed to improve Richards’ equation\nsimulations. Examples s
uch as the impoundment of a multi-material dam\nor the groundwater dynamic
s of sandy beaches illustrate the abilities\nof the approach.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:holidays
DTSTART;VALUE=DATE-TIME:20220308T080000Z
DTEND;VALUE=DATE-TIME:20220308T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/46
DESCRIPTION:by holidays as part of Necas PDE seminar\n\nLecture held in Bl
ue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Muha/ Collet GUILLOPÉ (University of Zagreb\, Universite Pa
ris-Est\,Creteil)
DTSTART;VALUE=DATE-TIME:20220315T080000Z
DTEND;VALUE=DATE-TIME:20220315T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/47
DESCRIPTION:Title: Poroelasticity Interacting with Stokes Flow/About a 1D Green - Naghdi
model with vorticity and surface tension for surface waves\nby Boris M
uha/ Collet GUILLOPÉ (University of Zagreb\, Universite Paris-Est\,Cretei
l) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute o
f Mathematics\,Zitna 25\,Prague.\n\nAbstract\nBoris Muha\, University of Z
agreb\nWe consider the interaction between an incompressible\, viscous flu
id\nmodeled by the dynamic Stokes equation and a multilayered poroelastic\
nstructure which consists of a thin\, linear\, poroelastic plate layer (in
direct contact with the free Stokes flow) and a thick Biot layer. The flu
id\nflow and the elastodynamics of the multilayered poroelastic structure
are\nfully coupled across a fixed interface through physical coupling cond
itions\n(including the Beavers-Joseph-Saffman condition)\, which present m
athematical challenges related to the regularity of associated velocity tr
aces.\nWe prove existence of weak solutions to this fluid-structure intera
ction\nproblem with either (i) a linear\, dynamic Biot model\, or (ii) a n
onlinear\nquasi-static Biot component\, where the permeability is a nonlin
ear function of the fluid content (as motivated by biological applications
). The\nproof is based on constructing approximate solutions through Rothe
’s\nmethod\, and using energy methods and a version of Aubin-Lions compa
ctness lemma (in the nonlinear case) to recover the weak solution as\nthe
limit of approximate subsequences. We also provide uniqueness criteria and
show that constructed weak solutions are indeed strong solutions\nto the
coupled problem if one assumes additional regularity.\nThe presented resul
ts are joint work with L. Bociu\, S. Canic and J.Webster\n\nGUILLOPÉ Cole
tte\nThe Green-Naghdi model is currently the most well-known model\nused f
or numerical simulations of waterfront streams\, even\nin setups that inco
rporate vanishing depth (at the shoreline) and wave\nbreaking. Regardless
of their many favorable circumstances\, the\nGreen-Naghdi equations specia
lly take into consideration neglected\nrotational effects\, which are sign
ificant for wind-driven waves\, waves\nriding upon a sheared current\, wav
es near a ship\, or tsunami waves\napproaching a shore. The Green-Naghdi s
ystem is first rewritten as an\nequivalent system by using an adequate
change\nof unknowns. We show that solutions to the model here considered\,
with\nvoracity and surface tension\, may be obtained by a standard Picard
\niterative scheme. No loss of regularity is involved with respect\nto the
initial data. Moreover solutions exist at the same level of\nregularity a
s\nfor 1rst order hyperbolic symmetric systems\, i.e. with a regularity in
\nSobolev spaces of order s > 3/2.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wroblewska
DTSTART;VALUE=DATE-TIME:20220322T080000Z
DTEND;VALUE=DATE-TIME:20220322T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/48
DESCRIPTION:Title: Two-phase compressible/incompressible Navier-Stokes system with inflow
-outflow boundary conditions\nby Wroblewska as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nI will show proof of the existence of a weak solution to
the compressible Navier-Stokes system with singular pressure that explodes
when density achieves its congestion level. This is a quantity whose init
ial value evolves according to the transport equation. We then prove that
the “stiff pressure" limit gives rise to the two-phase compressible/inco
mpressible system with congestion constraint describing the free interface
. We prescribe the velocity at the boundary and the value of density at th
e inflow part of the boundary of a general bounded C2 domain. For the posi
tive velocity flux\, there are no restrictions on the size of the boundary
conditions\, while for the zero flux\, a certain smallness is required fo
r the last limit passage. This result is based on a work with Milan Pokorn
ý and Ewelina Zatorska.\nReferences:\nM. Pokorný\, A. Wróblewska-Kamin
́ska\, E. Zatorska. Two-phase compressible/incompressible Navier–Stokes
system with inflow-outflow boundary conditions. arXiv:2202.03557\, 2022.\
n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ogorzaly
DTSTART;VALUE=DATE-TIME:20220405T070000Z
DTEND;VALUE=DATE-TIME:20220405T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/49
DESCRIPTION:by Ogorzaly as part of Necas PDE seminar\n\nLecture held in Bl
ue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Angeles Bellido (University of Sevilla)
DTSTART;VALUE=DATE-TIME:20220419T070000Z
DTEND;VALUE=DATE-TIME:20220419T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/50
DESCRIPTION:Title: Results for a bilinear control problem associated to a repulsive chemo
taxis model\nby Maria Angeles Bellido (University of Sevilla) as part
of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathemati
cs\,Zitna 25\,Prague.\n\nAbstract\nChemotaxis is understood as the biologi
cal process of the movement of living organisms in response to a chemical
stimulus which can be given towards a higher (attractive) or lower (repuls
ive) concentration of a chemical substance. At the same time\, the presenc
e of living organisms can produce or consume chemical substance.\nIn this
talk\, we study a bilinear optimal control problem associated to a chemo-r
epulsion model with linear production term in a 2D and 3D models. The exis
tence of a global optimal solution with bilinear control is analyzed. Firs
t-order optimality conditions for local optimal solutions are derived by u
sing a Lagrange multiplier theorem.\n\nReferences:\n\n[1] Guillén-Gonzál
ez\, F.\; Mallea-Zepeda\, E.\; Rodríguez-Bellido\, M. A.\nOptimal bilinea
r control problem related to a chemo-repulsion system in 2D domains.\nESAI
M Control Optim. Calc. Var. 26 (2020)\, Paper No. 29\, 21 pp.\n\n[2] Guill
en-Gonzalez\, F.\; Mallea-Zepeda\, E.\; Rodriguez-Bellido\, M. A.\nA regul
arity criterion for a 3D chemo-repulsion system and its application to a b
ilinear optimal control problem.\nSIAM J. Control Optim. 58 (2020)\, no. 3
\, 1457–1490.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:He (University of Bielefeld)
DTSTART;VALUE=DATE-TIME:20220517T070000Z
DTEND;VALUE=DATE-TIME:20220517T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/52
DESCRIPTION:Title: On some two-dimensional incompressible inhomogeneous viscous fluid flo
ws\nby He (University of Bielefeld) as part of Necas PDE seminar\n\nLe
cture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nA
bstract\nIn this talk\, we will present some existence\, uniqueness and re
gularity results for the motion of two-dimensional incompressible inhomoge
neous viscous fluid flows in presence of a density-/temperature-dependent
viscosity coefficient.\n\nFirstly\, we will discuss the boundary value pro
blem for the stationary Navier-Stokes equation\, where the viscosity coeff
icient is density-dependent. We will give some explicit solutions with pie
cewise constant viscosity coefficients\, where some regularity and irregul
arity results will be considered.\n\nWe will also discuss the initial valu
e problem for the evolutionary Boussinesq equation\, which is a nonlinear
coupling between a heat equation and a Navier-Stokes type of equation. In
this case\, the viscosity coefficient is temperature-dependent.\n\nThis ta
lk is based on joint work with Xian Liao (KIT).\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gudoshnikov
DTSTART;VALUE=DATE-TIME:20220222T080000Z
DTEND;VALUE=DATE-TIME:20220222T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/53
DESCRIPTION:Title: Sweeping process and its stability with applications to lattices of el
asto-plastic springs\nby Gudoshnikov as part of Necas PDE seminar\n\nL
ecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\n
Abstract\nMoreau's sweeping process is a class of non-smooth evolution pro
blems invented to handle one-sided constraints in natural processes involv
ing e.g. elastoplasticity\, friction and thresholds in electicity and elec
tomagnetism. The sweeping process can be viewed as a geometric generalizat
ion of hysteresis models.\nI will discuss its asymptotic properties\, espe
cially focusing on the case of a periodic input\, as it leads to periodic
outputs forming an attracting set.\nAnother focus will be the stress analy
sis of lattices of elasto-plastic springs via a finite-dimensional sweepin
g process (with illustrative examples). The mentioned asymptotic propertie
s lead to nice conclusions about stress trajectories in the lattice models
.\nThis is a joint project with Oleg Makarenkov\, Dmitry Rachinskiy (Unive
rsity of Texas at Dallas) and Yang Jiao (Arizona State University)."\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chebbi
DTSTART;VALUE=DATE-TIME:20220503T070000Z
DTEND;VALUE=DATE-TIME:20220503T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/55
DESCRIPTION:by Chebbi as part of Necas PDE seminar\n\nLecture held in Blue
Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huanyao Wen
DTSTART;VALUE=DATE-TIME:20220426T070000Z
DTEND;VALUE=DATE-TIME:20220426T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/56
DESCRIPTION:by Huanyao Wen as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Srdjan Trifunovic (University of Novi Sad)
DTSTART;VALUE=DATE-TIME:20220614T070000Z
DTEND;VALUE=DATE-TIME:20220614T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/57
DESCRIPTION:Title: Global existence of weak solutions in nonlinear 3D thermoelasticity\nby Srdjan Trifunovic (University of Novi Sad) as part of Necas PDE semi
nar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pra
gue.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Oschmann (Institute of Mathematics\, Czech Academy of Scie
nces)
DTSTART;VALUE=DATE-TIME:20221004T070000Z
DTEND;VALUE=DATE-TIME:20221004T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/58
DESCRIPTION:Title: An unexpected term for the Oberbeck--Boussinesq approximation\nby
Florian Oschmann (Institute of Mathematics\, Czech Academy of Sciences) as
part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mat
hematics\,Zitna 25\,Prague.\n\nAbstract\nThe Rayleigh-B\\'enard convection
problem deals with the motion\nof a compressible fluid in a tunnel heated
from below and cooled from\nabove. In this context\, the so-called Boussi
nesq relation is used\,\nclaiming that the density deviation from a consta
nt reference value is a\nlinear function of the temperature. These density
and temperature\ndeviations then satisfy the so-called Oberbeck-Boussines
q equations. The\nrigorous derivation of this system from the full compres
sible\nNavier-Stokes-Fourier system was done by Feireisl and Novotn\\'y fo
r\nconservative boundary conditions on the fluid's velocity and\ntemperatu
re. In this talk\, we investigate the derivation for Dirichlet\nboundary c
onditions\, and show that differently to the case of\nconservative boundar
y conditions\, the limiting system contains an\nunexpected non-local tempe
rature term. This is joint work with Peter\nBella (TU Dortmund) and Eduard
Feireisl (CAS).\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Simon (Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20221011T070000Z
DTEND;VALUE=DATE-TIME:20221011T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/59
DESCRIPTION:Title: CONVERGENCE OF SHAPE DESIGN SOLUTIONS FOR THE NAVIER–STOKES EQUATION
S\nby John Simon (Institute of Mathematics) as part of Necas PDE semin
ar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prag
ue.\n\nAbstract\nWe investigate the behavior of dynamic shape design probl
ems for fluid flow at large time horizon.\nIn particular\, we shall compar
e the solutions of a dynamic shape optimization problem with that of a sta
tionary\nproblem and show that the solution of the former converges to tha
t of the latter. The convergence of domains\nis based on the $L^\\infty$-t
opology of their corresponding characteristic functions which is closed un
der the\nset of domains satisfying the cone property. Lastly\, a numerical
example is provided to show the occurrence of such convergence.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Höfer (Université de Paris)
DTSTART;VALUE=DATE-TIME:20221101T080000Z
DTEND;VALUE=DATE-TIME:20221101T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/60
DESCRIPTION:Title: On the derivation of viscoelastic models for Brownian suspensions\
nby Richard Höfer (Université de Paris) as part of Necas PDE seminar\n\n
Lecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\
nAbstract\nWe consider effective properties of suspensions of inertialess\
, rigid\,\nanisotropic\, Brownian particles in Stokes flows. Recent years
have\nseen tremendous progress regarding the rigorous justification of\nef
fective fluid equations for non-Brownian suspensions\, where the\ncomplex
fluid can be described in terms of an effective viscosity. In\ncontrast to
this (quasi-)Newtonian behavior\, anisotropic Brownian\nparticles cause a
n additional elastic stress on the fluid. A rigorous\nderivation of such v
isco-elastic systems starting from particle models\nis completely missing
so far. In this talk I will present first\nresults in this direction start
ing from simplified microscopic models\nwhere the particles evolve only du
e to rotational Brownian motion and\ncause a Brownian torque on the fluid.
In the limit of infinitely many\nsmall particles with vanishing particle
volume fraction\, we rigorously\nobtain an elastic stress on the fluid in
terms of the particle density\nthat is given as the solution to an (in-)st
ationary Fokker-Planck\nequation.\nJoint work with Marta Leocata (LUISS Ro
me) and Amina Mecherbet\n(Université Paris Cité)\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elek Csobo
DTSTART;VALUE=DATE-TIME:20221108T080000Z
DTEND;VALUE=DATE-TIME:20221108T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/61
DESCRIPTION:by Elek Csobo as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helmut Abels (University of Regensburg)
DTSTART;VALUE=DATE-TIME:20221115T080000Z
DTEND;VALUE=DATE-TIME:20221115T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/62
DESCRIPTION:Title: Regularity and Convergence to Equilibrium for a Navier-Stokes-Cahn-Hil
liard System with Unmatched Densities\nby Helmut Abels (University of
Regensburg) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, In
stitute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe study the initia
l-boundary value problem for an incompressible Navier-Stokes-Cahn-Hilliard
system with non-constant density proposed by Abels\, Garcke and Grün in
2012. This model arises in the diffuse interface theory for binary mixtur
es of viscous incompressible fluids. This system is a generalization of th
e well-known model H in the case of fluids with unmatched densities. In th
ree dimensions\, we prove that any global weak solution (for which uniquen
ess is not known) exhibits a propagation of regularity in time and stabili
zes towards an equilibrium state as time tends to infinity. Our analysis h
inges upon the following key points: a novel global regularity result (wit
h explicit bounds) for the Cahn-Hilliard equation with divergence-free vel
ocity belonging only to the Leray-Hopf class\, the energy dissipation of t
he system\, the separation property for large times\, a weak strong unique
ness type result\, and the Lojasiewicz-Simon inequality.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY://
DTSTART;VALUE=DATE-TIME:20221018T070000Z
DTEND;VALUE=DATE-TIME:20221018T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/63
DESCRIPTION:by // as part of Necas PDE seminar\n\nLecture held in Blue Hal
l\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY://
DTSTART;VALUE=DATE-TIME:20221025T070000Z
DTEND;VALUE=DATE-TIME:20221025T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/64
DESCRIPTION:by // as part of Necas PDE seminar\n\nLecture held in Blue Hal
l\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Dębiec (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20221213T080000Z
DTEND;VALUE=DATE-TIME:20221213T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/65
DESCRIPTION:Title: On the incompressible limit for some tissue growth models\nby Toma
sz Dębiec (Sorbonne Université) as part of Necas PDE seminar\n\nLecture
held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstrac
t\nI will discus some approaches to mathematical modelling of\nliving tiss
ues\, with application to tumour growth. In particular\, I\nwill describe
recent results on to the incompressible limit of a\ncompressible model\, w
hich builds a bridge between density-based\ndescription and a geometric fr
ee-boundary problem by passing to the\nsingular limit in the pressure law.
\n \n The talk is divided in two parts. First\, I discuss the rate of\n co
nvergence of solutions of a general class of nonlinear diffusion\n equatio
ns of porous medium type to solutions of a Hele-Shaw-type\n problem. Then\
, I shall present a two-species tissue growth model —\n the main novelty
here is the coupling of both species through the\n so-called Brinkman law
which is typically used in the context of\n visco-elastic media\, where t
he velocity field is linked to the total\n population pressure via an elli
ptic equation.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthieu Cadiot (McGill University)
DTSTART;VALUE=DATE-TIME:20230214T080000Z
DTEND;VALUE=DATE-TIME:20230214T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/66
DESCRIPTION:Title: Rigorous Computation of Solutions of Semi-Linear Partial Differential
Equations on Unbounded Domains Via Spectral Methods\nby Matthieu Cadio
t (McGill University) as part of Necas PDE seminar\n\nLecture held in Blue
Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Mitra (Institute of Mathematics\,Czech Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20230221T080000Z
DTEND;VALUE=DATE-TIME:20230221T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/67
DESCRIPTION:Title: Existence of weak solutions for a compressible multi-component fluid s
tructure interaction problem\nby Sourav Mitra (Institute of Mathematic
s\,Czech Academy of Sciences) as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nI
will speak about our recent work on the analysis of a system of PDEs gove
rning the interaction between two compressible mutually noninteracting flu
ids and a shell of Koiter type encompassing\na time dependent 3D domain fi
lled by the fluids. The dynamics of the fluids is modelled by compressible
Navier-Stokes equations with a physically realistic pressure depending on
densities of both the fluids.\nThe shell constitutes the boundary of the
fluid domain and it possesses a non-linear\, non-convex Koiter energy (of
a quite general form). We are interested in the existence of a weak soluti
on to the system until the time-dependent boundary approaches a self-inter
section. We first prove a global existence result (until a degeneracy occu
rs) when the structure in hyperbolic\, the adiabatic exponents solve max{
γ\, β} > 2 2 and min{γ\, β} > 0. and further the initial densities ar
e comparable. Next with an extra assumption that the structure is dissipat
ive\, we extend our global existence result to the case max{γ\, β} ≥ 2
and min{γ\, β} > 0.\nIn the first part of the talk I will try to recall
a little the classical theory on the existence of weak solutions for comp
ressible mono-fluid models. Next I will talk about our work on the multi-c
omponent FSI problem. It is a joint work with M.Kalousek and S.Necasova\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Gudoshnikov (Institute of Mathematics\, Czech Academy of Scie
nces)
DTSTART;VALUE=DATE-TIME:20230228T080000Z
DTEND;VALUE=DATE-TIME:20230228T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/68
DESCRIPTION:by Ivan Gudoshnikov (Institute of Mathematics\, Czech Academy
of Sciences) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, I
nstitute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aneta Wroblewska (Institute of Mathematics\,Polish Academy of Scie
nces)
DTSTART;VALUE=DATE-TIME:20230307T080000Z
DTEND;VALUE=DATE-TIME:20230307T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/69
DESCRIPTION:Title: Relaxation limit of hydrodynamic models\nby Aneta Wroblewska (Inst
itute of Mathematics\,Polish Academy of Sciences) as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\n\nAbstract\nWe will show how to obtain general nonlinear aggregatio
n-diffusion models\,\nincluding Keller-Segel type models with nonlinear di
ffusions\, as\nrelaxations from nonlocal compressible Euler-type hydrodyna
mic systems via\nthe relative entropy method. We plan to discuss the assum
ptions on the\nconfinement and interaction potentials depending on the rel
ative energy of\nthe free energy functional allowing for this relaxation l
imit to hold. We\nwill deal with weak solutions for the nonlocal compressi
ble Euler-type\nsystems and strong solutions for the limiting aggregation-
diffusion\nequations. Finally\, we will mention how to show the existence
of weak\nsolutions to the nonlocal compressible Euler-type systems satisfy
ing the\nneeded properties for completeness sake. This is a joint result w
ith Jose\nCarrillo and Yingping Peng.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mikhailets (Institute of Mathematics\,Czech Academy of S
ciences)
DTSTART;VALUE=DATE-TIME:20230314T080000Z
DTEND;VALUE=DATE-TIME:20230314T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/70
DESCRIPTION:Title: One-dimensional differential operators with distributions in coefficie
nts\nby Volodymyr Mikhailets (Institute of Mathematics\,Czech Academy
of Sciences) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, I
nstitute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nSome classes of li
near ordinary differential operators with strongly singular coefficients a
re studied in the talk. These operators are introduced as quasi-differenti
al according to Shin-Zettl. Their domains may not contain non-zero smooth
functions. The case of self-adjoint Schr\\"{o}dinger and Hill operators on
the line is investigated in more detail.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Eiter (Weisstrass Institute\,Berlin)
DTSTART;VALUE=DATE-TIME:20230328T070000Z
DTEND;VALUE=DATE-TIME:20230328T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/71
DESCRIPTION:Title: The concept of energy-variational solutions for hyperbolic conservatio
n laws\nby Thomas Eiter (Weisstrass Institute\,Berlin) as part of Neca
s PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zit
na 25\,Prague.\n\nAbstract\nWe consider the notion of energy-variational s
olutions for hyperbolic\nconservation laws. This novel solvability concept
is obtained by\nenriching the variational formulation by the weighted dif
ference\nbetween the mechanical energy and an auxiliary variable represent
ing\nthe turbulent energy. If the weight is chosen suitably\, an existence
\nresult for a general class of conservation laws can be derived via a\nti
me-discretization scheme based on a sequential minimization and\, in\npart
icular\, without a spatial regularization. The solution concept\ncomes alo
ng with favorable properties like a weak-strong uniqueness\nprinciple and
the convexity of solution sets. Moreover\, for the\ncompressible and incom
pressible Euler equations\, energy-variational\nsolutions can be identifie
d with dissipative weak solutions.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbatiello\, Chaudhuri\, Fasangova
DTSTART;VALUE=DATE-TIME:20230404T070000Z
DTEND;VALUE=DATE-TIME:20230404T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/72
DESCRIPTION:by Abbatiello\, Chaudhuri\, Fasangova as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduard Feireisl (Institute of Mathematics\, Czech Academy of Scien
ces)
DTSTART;VALUE=DATE-TIME:20230411T070000Z
DTEND;VALUE=DATE-TIME:20230411T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/73
DESCRIPTION:Title: Compressible MHD as a dissipative system\nby Eduard Feireisl (Inst
itute of Mathematics\, Czech Academy of Sciences) as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\n\nAbstract\nWe show that the compressible MHD system admits a bound
ed absorbing\nset in the energy ``norm'' as long as the open boundary\ncon
ditions are imposed. In addition\, the trajectories are precompact\nin a s
uitable topology. If this is the case\, there is a compact global\nattract
or as well as statistical stationary solutions supported by\nindividual tr
ajectories of weak solutions.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonin Cesik (Faculty of Mathematics and Physics)
DTSTART;VALUE=DATE-TIME:20230321T080000Z
DTEND;VALUE=DATE-TIME:20230321T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/74
DESCRIPTION:Title: Inertial evolution of non-linear viscoelastic solids in the face of (s
elf-)collision\nby Antonin Cesik (Faculty of Mathematics and Physics)
as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of M
athematics\,Zitna 25\,Prague.\n\nAbstract\nThe talk discusses existence th
eory for collisions of (visco-)elastic\nbulk solids which are undergoing i
nertial evolution. In particular\,\nour approach for contact is based only
on the assumption of\nnon-interpenetration of matter. Most other theories
for contact of\nelastic solids include some phenomenological assumptions\
, which we do\nnot need in our approach.\n\nWe are able to show existence
of weak solutions including contact with\nan obstacle or with the solid it
self\, for arbitrarily large times and\nlarge deformations. Furthermore\,
our construction includes a\ncharacterization of the contact force which o
beys conservation of\nmomentum and an energy balance. This contact force i
s a vector-valued\nsurface measure acting in the normal direction\, and is
constructed as\na consequence of the non-interpenetration of matter.\nThi
s is a joint work with Giovanni Gravina and Malte Kampschulte.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Oschmann (Institute of Mathematics\,Czech Academy of Scien
ces)
DTSTART;VALUE=DATE-TIME:20230502T070000Z
DTEND;VALUE=DATE-TIME:20230502T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/75
DESCRIPTION:by Florian Oschmann (Institute of Mathematics\,Czech Academy o
f Sciences) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, In
stitute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART;VALUE=DATE-TIME:20230509T070000Z
DTEND;VALUE=DATE-TIME:20230509T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/76
DESCRIPTION:Title: Introduction to free boundary problem for the Navier-Stokes equations
and R-solver approach to this problem\nby Yoshihiro Shibata (Waseda Un
iversity) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Inst
itute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThis is first lecture
in the series of three lectures by Prof. Shibata.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART;VALUE=DATE-TIME:20230516T063000Z
DTEND;VALUE=DATE-TIME:20230516T073000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/77
DESCRIPTION:Title: Maximal L_p-L_q theory for the Stokes equations with free boundary con
ditions\nby Yoshihiro Shibata (Waseda University) as part of Necas PDE
seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25
\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University)
DTSTART;VALUE=DATE-TIME:20230523T070000Z
DTEND;VALUE=DATE-TIME:20230523T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/78
DESCRIPTION:Title: Local and global well-posedness of free boundary problem for the Navie
r-Stokes equations in exterior domains.\nby Yoshihiro Shibata (Waseda
University) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, In
stitute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Kaplicky (Charles University)
DTSTART;VALUE=DATE-TIME:20230418T070000Z
DTEND;VALUE=DATE-TIME:20230418T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/79
DESCRIPTION:Title: Stokes problems with dynamic boundary conditions\nby Petr Kaplicky
(Charles University) as part of Necas PDE seminar\n\nLecture held in Blue
Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe show m
aximal regularity in time of solutions to the\nevolutionary Stokes problem
with dynamic boundary condition in the\ncase that the underlying space is
Hilbert space.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maja Szlenk (Warsaw University)
DTSTART;VALUE=DATE-TIME:20230425T070000Z
DTEND;VALUE=DATE-TIME:20230425T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/80
DESCRIPTION:by Maja Szlenk (Warsaw University) as part of Necas PDE semina
r\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pragu
e.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Caggio (Institute of Mathematics\, Czech Academy of Science
s)
DTSTART;VALUE=DATE-TIME:20231003T070000Z
DTEND;VALUE=DATE-TIME:20231003T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/81
DESCRIPTION:Title: Inviscid limit for the compressible Navier-Stokes equations with densi
ty dependent viscosity\nby Matteo Caggio (Institute of Mathematics\, C
zech Academy of Sciences) as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe co
nsider the compressible Navier-Stokes system describing the motion of a ba
rotropic\nfluid with density dependent viscosity confined in a three-dimen
sional bounded domain.\nWe show the convergence of the weak solution to th
e compressible Navier-Stokes system to the strong\nsolution to the compres
sible Euler system when the viscosity and the damping coefficients tend to
zero.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yadong Liu (University of Regensburg)
DTSTART;VALUE=DATE-TIME:20231114T080000Z
DTEND;VALUE=DATE-TIME:20231114T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/82
DESCRIPTION:Title: On a compressible fluid-structure interaction problem with slip bounda
ry conditions\nby Yadong Liu (University of Regensburg) as part of Nec
as PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zi
tna 25\,Prague.\n\nAbstract\nIn this talk\, I will present a project on a
compressible barotropic fluid system interacting with a linear (visco)-ela
stic solid equation. In particular\, the elastic structure formulates the
moving boundary of the fluid\, and the Navier-slip type boundary condition
is taken into account. Depending on the reference geometry (flat or not)\
, I will present the existence of weak solutions to the coupled system pro
vided the adiabatic exponent satisfies $\\gamma > \\frac{12}{7}$ without d
amping and $\\gamma > \\frac{3}{2}$ with structure damping. Moreover\, via
a modified relative entropy method in time-dependent domains\, I will sho
w you the weak-strong uniqueness property of weak solutions. Finally\, I w
ill give a rigorous justification of the incompressible inviscid limit of
the compressible fluid-structure interaction problem with a flat reference
geometry\, in the regime of low Mach number\, high Reynolds number\, and
well-prepared initial data. This talk is based on joint work with Sourav M
itra (IIT\, Indore) and Šárka Nečasová (IMCAS\, Prague).\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyu Liang (LMU Munich\,Germany)
DTSTART;VALUE=DATE-TIME:20231121T080000Z
DTEND;VALUE=DATE-TIME:20231121T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/83
DESCRIPTION:Title: White noise solutions to mSQG equations\nby Siyu Liang (LMU Munich
\,Germany) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Ins
titute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe show existence o
f white noise solutions for weak\nformulations of modified Surface Qu
asi-Geostrophic (mSQG) equations.\n Based on previous results on white no
ise solutions for mSQG\nequations on the torus T^2\, we show a similar r
esult for the whole\nspace R^2 by letting the volume of the torus go to in
finity and\napplying compactness methods (Skorokhod's theorem).\nWe will p
resent the details on how the kernel on T^2 converges to the\nkernel on R^
2.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Sokolowski
DTSTART;VALUE=DATE-TIME:20231128T080000Z
DTEND;VALUE=DATE-TIME:20231128T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/84
DESCRIPTION:by Jan Sokolowski as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neslihan Nesliye Pelen (Ondokuz Mayıs University)
DTSTART;VALUE=DATE-TIME:20240109T080000Z
DTEND;VALUE=DATE-TIME:20240109T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/85
DESCRIPTION:Title: Vector-Borne Disinformation During Disasters and Emergencies\nby N
eslihan Nesliye Pelen (Ondokuz Mayıs University) as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\n\nAbstract\nDuring disasters and emergencies (earthquakes\, pandemi
cs\, economic crises\, etc.)\, we also face a second challenge: informatio
n pollution. The transmitted information may be false\, potentially harmfu
l\, and speculative. Today\, the main source of information is social medi
a\, which behaves as a vector via sharing news. In this presentation\, the
concept of the transmission dynamics of vector-borne diseases is adapted
to the transmission dynamics of vector-borne disinformation. The dynamical
behavior of the model is analyzed\, the disinformation-free and disinform
ation-endemic equilibria of the model are found\, and both their local and
global stabilities are also discussed. Numerical simulations are also car
ried out to support the analytical results of the dynamical transmission o
f disinformation.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Scherz (University of Würzburg/Charles University)
DTSTART;VALUE=DATE-TIME:20240109T091000Z
DTEND;VALUE=DATE-TIME:20240109T094000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/86
DESCRIPTION:Title: Weak Solutions to Mathematical Models of the Interaction between Fluid
s\, Solids and Electromagnetic Fields\nby Jan Scherz (University of W
ürzburg/Charles University) as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe
prove the existence of weak solutions to two systems of PDEs modeling int
eractions between fluids\, solids and electromagnetic fields. The first pr
oblem we consider describes the motion of an insulating rigid body through
an electrically conducting incompressible fluid. The existence of weak so
lutions to this problem is achieved via a time discretization and an appli
cation of the Brinkman penalization. The second considered problem deals w
ith the evolution of the deformation and the magnetization of a magnetoela
stic material and is solved via an application of De Giorgi's minimizing m
ovements scheme.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Gavioli
DTSTART;VALUE=DATE-TIME:20240220T080000Z
DTEND;VALUE=DATE-TIME:20240220T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/87
DESCRIPTION:by Chiara Gavioli as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisabeta Rocca (University of Pavia)
DTSTART;VALUE=DATE-TIME:20240521T063000Z
DTEND;VALUE=DATE-TIME:20240521T073000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/88
DESCRIPTION:Title: From non local to local Cahn-Hilliard-Reaction-Diffusion model for tum
or growth\nby Elisabeta Rocca (University of Pavia) as part of Necas P
DE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna
25\,Prague.\n\nAbstract\nIn this seminar we discuss about a recent joint w
ork with Elisa Davoli\,\nLuca Scarpa and Lara Trussardi where we study a n
onlocal-to-local\nasymptotics for a tumor-growth model coupling a viscous
Cahn-Hilliard\nequation describing the tumor proportion with a reaction-di
ffusion\nequation for the nutrient phase parameter. First\, we prove that\
nsolutions to the nonlocal Cahn-Hilliard system converge\, as the\nnonloca
lity parameter tends to zero\, to solutions to its local\ncounterpart. Sec
ond\, we provide first-order optimality conditions for an\noptimal control
problem on the local model\, accounting also for\nchemotaxis\, and both f
or regular or singular potentials\, without any\nadditional regularity ass
umptions on the solution operator.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Simon (Austrian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20240305T080000Z
DTEND;VALUE=DATE-TIME:20240305T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/89
DESCRIPTION:Title: Analysis of Unregularized Optimal Control Problems Constrained by the
Boussinesq System\nby John Simon (Austrian Academy of Sciences) as par
t of Necas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathema
tics\,Zitna 25\,Prague.\n\nAbstract\nWe investigate solution stability of
unregularized tracking-type optimal control problems constrained by the Bo
ussinesq system. In our model\, the controls may appear linearly and distr
ibuted in both of the equations that constitute the Boussiniesq system and
in the objective functional. We establish\, not only the existence of wea
k solutions\, but also unique existence of strong solutions in $L^p$ sense
for the Boussinesq system as well as its corresponding linearized and adj
oint systems. The optimal control problem is then analyzed by providing th
e existence of an optimal control\, and by establishing first-order necess
ary and second order sufficient conditions. Then\, using assumptions on th
e joint growth of the first and second variations of the objective functio
nal\, we prove the strong metric Hölder subregularity of the optimality m
apping\, which in turn allows the study of solution stability of the optim
al control and states under various linear and nonlinear perturbations. Su
ch perturbations may appear in the Boussinesq system and the objective fun
ctional. As an application\, we provide a convergence rate for the optimal
solutions of the Tikhonov regularized problem as the Tikhonov parameter t
ends to zero. Furthermore\, the obtained stability of the optimal states p
rovides stability of the second-order sufficient condition in affine PDE-c
onstrained optimization under an assumption on the desired profile which i
s natural for tracking-type objective functionals.\n\n\n\nThis is a joint
work with Nicolai Jork.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Lancmanova (Czech Technical University)
DTSTART;VALUE=DATE-TIME:20240312T080000Z
DTEND;VALUE=DATE-TIME:20240312T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/90
DESCRIPTION:Title: Numerical Study of the Steady Airflow in the Human Respiratory System
During Inhaling and Exhaling\nby Anna Lancmanova (Czech Technical Univ
ersity) as part of Necas PDE seminar\n\nLecture held in Blue Hall\, Instit
ute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nThis paper presents som
e of the initial results of the numerical simulations of a steady turbulen
t flow in human upper airways during inhalation and exhalation. The mathem
atical model is based on the system of Reynolds-Averaged incompressible Na
vier-Stokes equations complemented by the SST k − ω turbulence model. T
he simulations were performed using the finite-volume open-source solver O
penFOAM on a realistic three-dimensional geometry. The main aim of this pa
rticular study is to verify the computational setup with a special focus o
n the appropriate choice and implementation of boundary conditions. The pr
escribed boundary conditions are chosen to mimic the physiological conditi
ons during a normal breathing cycle. This study aims to gain insight into
the airflow behavior during the inhalation and exhalation process by compa
ring the results of two distinct simulations corresponding to two differen
t (opposite) flow rates. The obtained local flow rates and flow fields for
both cases are presented and mutually compared. This initial work should
serve as a foundation for future more complex simulations that will includ
e the time-dependent and compressible effects.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomas Roubicek
DTSTART;VALUE=DATE-TIME:20240326T080000Z
DTEND;VALUE=DATE-TIME:20240326T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/91
DESCRIPTION:Title: Thermomechanical models for finitely-strained viscoelastic solids and
related mathematical aspects\nby Tomas Roubicek as part of Necas PDE s
eminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,
Prague.\n\nAbstract\nModels of visco-elastodynamic solids at finite strain
s will be presented and the Lagrangian versus Eulerian formulation will be
discussed. Mathematical analysis using some gradient theories will be out
lined and some impacts of these higher gradients on dispersion and attenua
tion of wave propagation will be discussed\, too. Also coupled thermomecha
nical problems will be presented\, allowing for heat capacity degenerating
to zero at zero temperature\, which is also a physically relevant attribu
te related with non-negativity of entropy.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Neustupa (Institute of Mathematics\,Czech Academy of Sciences
)
DTSTART;VALUE=DATE-TIME:20240402T070000Z
DTEND;VALUE=DATE-TIME:20240402T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/92
DESCRIPTION:Title: On steady solutions to the MHD equations with inhomogeneous generalize
d impermeability boundary conditions for the magnetic field\nby Jiri N
eustupa (Institute of Mathematics\,Czech Academy of Sciences) as part of N
ecas PDE seminar\n\nLecture held in Blue Hall\, Institute of Mathematics\,
Zitna 25\,Prague.\n\nAbstract\nWe deal with the steady MHD equations for a
viscous incompressible fluid with the no--slip boundary condition for the
velocity $u$ and the inhomogeneous version of the so called generalized i
mpermeability boundary conditions for the magnetic field $b$. We explain t
he sense of these conditions. The main results concern an appropriate defi
nition of the weak solution $(u\,b)$\, its existence\, continuous dependen
ce on the data when the data tend to zero and uniqueness in a ``small'' ne
ighborhood of the zero solution $u=0$\, $b=0$.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rinaldo Colombo (University of Brescia)
DTSTART;VALUE=DATE-TIME:20240409T070000Z
DTEND;VALUE=DATE-TIME:20240409T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/93
DESCRIPTION:Title: Hyperbolic Techniques in Biological Models\nby Rinaldo Colombo (Un
iversity of Brescia) as part of Necas PDE seminar\n\nLecture held in Blue
Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nConservati
on (or Balance) Laws enter a variety of biological\nmodels. In population
dynamics\, balance laws describe age (or space)\nstructured dynamics. In e
pidemiology\, balance laws enter several\nvariazioni on the SIR model. In
predator prey dynamics\, non local\nbalance laws describe species moving w
ith finite speed towards a well\ndefined target. Other examples of the use
of these equations are\nprovided by cancer or cell growth.\n\nThis talk p
resents some analytical results related to the the above\nmodels\, hoping
to foster the discussion also on the modeling and on\nthe numerical issues
involved.\n\nJoint work with M. Garavello (University of Milano - Bicocca
)\,\nF. Marcellini (University of Brescia) and E. Rossi (University of\nMo
dena - Reggio Emilia).\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Hajduk
DTSTART;VALUE=DATE-TIME:20240416T070000Z
DTEND;VALUE=DATE-TIME:20240416T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/94
DESCRIPTION:by Karol Hajduk as part of Necas PDE seminar\n\nLecture held i
n Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Caggio (Institute of Mathematics\, Czech Academy of Science
s)
DTSTART;VALUE=DATE-TIME:20240507T070000Z
DTEND;VALUE=DATE-TIME:20240507T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/96
DESCRIPTION:Title: Vanishing viscosity limit for the compressible Navier-Stokes equations
with non-linear density dependent viscosities\nby Matteo Caggio (Inst
itute of Mathematics\, Czech Academy of Sciences) as part of Necas PDE sem
inar\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pr
ague.\n\nAbstract\nIn a three-dimensional bounded domain\, we consider the
compressible\nNavier-Stokes equations\nfor a barotropic fluid with genera
l non-linear density dependent\nviscosities and no-slip boundary\nconditio
ns. A nonlinear drag term is added to the momentum equation.\nWe establish
two\nconditional Kato-type criteria for the convergence of the weak\nsolu
tions to such a system\ntowards the strong solution of the compressible Eu
ler system when the\nviscosity coefficient\nand the drag term parameter te
nd to zero.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Imene DJEBOUR (CY Cergy–Paris Université)
DTSTART;VALUE=DATE-TIME:20240604T070000Z
DTEND;VALUE=DATE-TIME:20240604T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/97
DESCRIPTION:Title: Existence of strong solutions for a compressible fluid-solid interacti
on system with Navier slip boundary conditions\nby Imene DJEBOUR (CY C
ergy–Paris Université) as part of Necas PDE seminar\n\nLecture held in
Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nWe co
nsider a fluid-structure interaction system coupling a viscous\nfluid gove
rned by the compressible Navier-Stokes equations and a rigid\nbody immerse
d in the fluid and modeled by the Newton's law. In this\nwork\, we conside
r the Navier slip boundary conditions. Our aim is to\nshow the local in ti
me existence and uniqueness of the strong solution\nto the corresponding p
roblem. The main step of this work is that we use\nLagrangian change of va
riables in order to handle the transport equation\nand to reduce the probl
em in the initial domain. The strategy is based\non the study of the linea
rized system with nonhomogeneous boundary\nconditions and on the Banach fi
xed point theorem.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akash Parmar (University of Warsaw)
DTSTART;VALUE=DATE-TIME:20240507T082000Z
DTEND;VALUE=DATE-TIME:20240507T092000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/98
DESCRIPTION:Title: Optimal regularity for conservation laws with discontinuous flux an
d large data existence for the isentropic Euler equations\nby Akash Pa
rmar (University of Warsaw) as part of Necas PDE seminar\n\nLecture held i
n Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\n\nAbstract\nIn
this talk\, first\, we discuss the regularity aspects of the scalar\nconse
rvation laws with discontinuous flux. The optimal regularity of the\nentro
py solution has been an open question since 2011 [Adimurthi et. al\,\nComm
. Pure Appl. Math.\, 2011]\, as they established that the entropy\nsolutio
n of scalar conservation laws with discontinuous flux does not\nbelong to
BV space even when the initial data is in BV. We prove the\noptimal regula
rity of the entropy solution for bounded initial data in\nthe "fractional
BV" space\, (i.e.\, we prove the Lax-Oleinik type\nregularizing effect).
Furthermore\, we demonstrate the higher regularity\nof the entropy soluti
on in the "fractional BV" space for the\ngeometrically restricted fluxes.
In the second part of the talk\, we\ndiscuss the global existence of a we
ak solution for the isentropic Euler\nequation in one space dimension with
large initial data in BV. We use\nGlimm's scheme to get the approximate w
eak solution and then Riemann\ninvariant to get the uniform bounds of the
total variation. We also\nprovide a criterion under which the total variat
ion of Riemann\ninvariants decays.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Kaplicky
DTSTART;VALUE=DATE-TIME:20240430T070000Z
DTEND;VALUE=DATE-TIME:20240430T080000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/99
DESCRIPTION:by Petr Kaplicky as part of Necas PDE seminar\n\nLecture held
in Blue Hall\, Institute of Mathematics\,Zitna 25\,Prague.\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong Lyu (Nanjing University)
DTSTART;VALUE=DATE-TIME:20240521T080000Z
DTEND;VALUE=DATE-TIME:20240521T090000Z
DTSTAMP;VALUE=DATE-TIME:20240910T011159Z
UID:TuesdayPDE/100
DESCRIPTION:Title: Unconditional stability of equilibria in thermally driven compressibl
e fluids\nby Yong Lyu (Nanjing University) as part of Necas PDE semina
r\n\nLecture held in Blue Hall\, Institute of Mathematics\,Zitna 25\,Pragu
e.\n\nAbstract\nWe show that small perturbations of the spatially homogene
ous equilibrium of a thermally driven compressible viscous fluid are globa
lly stable. Specifically\, any weak solution of the evolutionary Navier-St
okes-Fourier system driven by thermal convection converges to an equilibri
um as time goes to infinity. The main difficulty to overcome is the fact t
he problem does not admit any obvious Lyapunov function. The result applie
s\, in particular\, to the Rayleigh-Bénard convection problem.\n
LOCATION:https://researchseminars.org/talk/TuesdayPDE/100/
END:VEVENT
END:VCALENDAR