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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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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
DTSTART;VALUE=DATE-TIME:20220517T070000Z
DTEND;VALUE=DATE-TIME:20220517T080000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201003Z
UID:TuesdayPDE/52
DESCRIPTION:by He 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/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gudoshnikov
DTSTART;VALUE=DATE-TIME:20220222T080000Z
DTEND;VALUE=DATE-TIME:20220222T090000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201003Z
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:20220528T201003Z
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:20220528T201003Z
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
END:VCALENDAR