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BEGIN:VEVENT
SUMMARY:G.Paolo Galdi (University of Pittsburgh\, USA)
DTSTART;VALUE=DATE-TIME:20201112T130000Z
DTEND;VALUE=DATE-TIME:20201112T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/1
DESCRIPTION:Title: On the Self-Propelled Motion of a Rigid Body in a Viscous
Liquid by Time-Periodic Boundary Data\nby G.Paolo Galdi (University of
Pittsburgh\, USA) as part of Fudan International Seminar on Analysis\, PD
Es\, and Fluid mechanics\n\n\nAbstract\nWe consider a body\, $\\mathcal B$
\, moving in a Navier-Stokes liquid and subject to a driving\nmechanism co
nstituted by a time-periodic distribution of velocity\, $\\mathbf v_*$\, a
t the interface\nbody-liquid. This study is mostly motivated by understand
ing the vibration-induced\npropulsion of objects of fixed shape moving in
a viscous liquid. More precisely\, we aim\nat characterizing the thrust an
d its relation to the translational velocity of $\\mathcal B$. With\nthis
in mind\, we show that\, in a suitable class of weak solutions\, if the av
erage over a\nperiod of $\\mathbf v_*$\, $\\bar\\mathbf v_*$ is not zero\,
then $\\mathcal B$ will propel itself on the condition that $\\bar\\mathb
f v_*$ has a non-vanishing projection on a suitable “control” space. T
his result is achieved by using a suitable perturbation argument around a
linearized solution. If\, however\, $\\bar\\mathbf v_*=0$ (purely oscillat
ory case\, like in the vibration-induced motion)\, we then show that self-
propulsion is a strictly nonlinear phenomenon and that it occurs if and on
ly if $\\bar\\mathbf v_*$ satisfies a suitable non-local condition.\n\nThe
recorded talk is available\, see the above link\, Passcode: X!Pi=V2A\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Panasenko (Institute Camille Jordan UMR CNRS 5208\, Univer
sity Jean Monnet\, Saint-Etienne\, France)
DTSTART;VALUE=DATE-TIME:20201203T130000Z
DTEND;VALUE=DATE-TIME:20201203T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/2
DESCRIPTION:Title: Asymptotic coupling of models of different dimensions: MAP
DD\nby Grigory Panasenko (Institute Camille Jordan UMR CNRS 5208\, Uni
versity Jean Monnet\, Saint-Etienne\, France) as part of Fudan Internation
al Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nThe lec
ture is devoted to the problem of coupling of models of different dimensio
n. Many real world problems are related to solving partial differential eq
uations in domains of complex geometry\, combining multiple thin parts wit
h massive parts: the set of blood vessels\, structures in aircraft and spa
cecraft\, industrial installations\, pipelines with reservoirs. The direct
numerical computations with standard codes are impossible because such co
mplex geometry needs a very fine mesh “feeling” all elements of the st
ructure and so the 3D computations need too much time-memory resources. Th
at is why the dimension reduction is a very popular trend in reducing comp
utational cost\, however the completely reduced model loses very important
local information and are not precise. For example\, in the blood circula
tion modelling [1] one-dimensional models are widely applied\, but the des
cription of the clot formation\, blood flow near a stent need 3D local zoo
m. How to glue the models of different dimension? The lecture presents an
asymptotic approach to this problem\, based on asymptotic analysis of part
ial differential equations in domains containing thin parts\, connected se
ts of thin cylinders. For example the Navier-Stokes equations are used in
hemodynamic modeling. We present the method of partial asymptotic decompos
ition of domains (MAPDD) [2-6] giving a high precision coupling of models
of different dimension.\n \nFormaggia\,L.\, Quarteroni\,A.\, Veneziani A
.\, Cardiovascular Mathematics: Modeling and simulation of the circulatory
system\, Springer Science and Business Media\, 2010.\n2.
Panasenko G.\, Method of asymptotic partial decomposition of domain\
, Mathematical Models and Methods in Applied Sciences \, 8\,1\, 1998\, 139
-156.\nPanasenko G.\, Multi-Scale Modelling for Structures and Composites\
, Springer\, Dordrecht\, 2005. \nPanasenko G.\, Method of asymptotic part
ial decomposition of domain for multistructures\, Applicable Analysis\, 20
17\, 96\, 16\, 2771-2779\, http://dx.doi.org/10.1080/00036811.2016.1240366
\nPanasenko G.\, Pileckas K.\, Asymptotic analysis of the non-steady Navie
r-Stokes equations in a tube structure.I. The case without boundary layer-
in-time. Nonlinear Analysis\, Series A\, Theory\, Methods and Applications
\, 122\, 2015\, 125-168\, http://dx.doi.org/10.1016/j.na.2015.03.008\nBert
oglio C.\, Conca C.\, Nolte D.\, Panasenko G.\, Pileckas K.\, Junction of
models of different dimension for flows in tube structures by Womersley-ty
pe interface conditions\, SIAM J. Appl.Math. 2019 79\, 3\, 959-985 doi.10.
1137/M1229572\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Volberg (Michigan State University)
DTSTART;VALUE=DATE-TIME:20201119T130000Z
DTEND;VALUE=DATE-TIME:20201119T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/3
DESCRIPTION:Title: Removable singularities for Lipschitz harmonic functions\,
Geometric Measure Theory\, and fine structure of harmonic measure\nby
Alexander Volberg (Michigan State University) as part of Fudan Internatio
nal Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWhat a
re the removable singularities of harmonic functions with bounded gradient
? This problem\, that takes its origins in certain problems of complex an
alysis\, which are 140 years old was solved recently. It is a free boundar
y problem and its solution (which we will explain) is based on extension t
o a new territory of classical theory of singular integrals.\nSingular int
egrals are ubiquitous objects. The simplest ones are called Calderon–Zyg
mund operators. Their theory was completed in the 50′s by Zygmund and Ca
lderon. Or it seemed like that. The last 20 years saw the need to consider
CZ operators in\nvery bad environment\, so kernels are still very good\,
but the ambient set/measure has no regularity whatsoever.\nInitially\, suc
h situations appeared from the wish to solve some outstanding problems in
complex analysis: such as problems of Painlev\\’e\, Ahlfors’\, Denjoy
’s\, and Vitushkin’s.\nThe analysis of CZ operators on very bad sets i
s also very fruitful in the part of Geometric Measure Theory that deals wi
th removability mentioned above and rectifiability. It can be viewed as th
e study of very low regularity free boundary problems. We will explain th
e genesis of ideas that led to several long and difficult proves that culm
inated in our solution to problems of Denjoy\, Vitushkin and Guy David\, a
nd also brought the solution by Tolsa of Painlev\\’e’s problem.\n\nThe
passcode to the recorded video is\n^98qdTub\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao Ren (任潇) (Fudan University)
DTSTART;VALUE=DATE-TIME:20201126T130000Z
DTEND;VALUE=DATE-TIME:20201126T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/4
DESCRIPTION:Title: The uniqueness of Plane Stationary Navier-Stokes Flow Past
an Obstacle\nby Xiao Ren (任潇) (Fudan University) as part of Fudan
International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstr
act\nWe study the exterior problem for stationary Navier-Stokes equations
in two dimensions describing a viscous incompressible fluid flowing past a
n obstacle. It is shown that\, at small Reynolds numbers\, the classical s
olutions constructed by Finn and Smith are unique in the class of D-soluti
ons (i.e.\, solutions with finite Dirichlet integral). No additional symme
try or decay assumptions are required. This result answers a long-standing
open problem. The talk is based on a joint paper with M.Korobkov.\n\nThe
passcode for the recorded video\n=$!02mLv\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shnirelman (Concordia University\, Montreal\, Quebec\, C
anada)
DTSTART;VALUE=DATE-TIME:20201210T130000Z
DTEND;VALUE=DATE-TIME:20201210T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/5
DESCRIPTION:Title: Turbulent weak solutions of the Euler equations\nby Al
exander Shnirelman (Concordia University\, Montreal\, Quebec\, Canada) as
part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechani
cs\n\n\nAbstract\nTurbulence is the property of flows of an incompressible
fluid at very high Reynolds number\, or\, equivalently\, at very small vi
scosity. The most prominent feature of turbulent flows is a considerable r
ate of the energy dissipation which is nearly independent on the viscosity
provided the latter is small enough. It is natural to consider the case o
f infinitesimally small viscosity in the hope that there exists a meaningf
ul limit of viscous flows as the viscosity tends to zero. In the limit the
flows are described by some sort of weak solutions of the Euler equations
. However\, there exist a lot of examples of weak solutions (Scheffer\, Sh
nirelman\, De Lellis\, Szekekyhidi\, Buckmaster\, Vicol\, and others) whos
e behavior is far from what is expected from the models of turbulent flows
. Those weak solutions are definitely non-physical.\n \n\nIn this talk I'm
going to describe a new class of weak solutions of the Euler equations wh
ich might have more physical content. Their construction is based on the c
ombination of several ideas: (a) Comprehensive Lagrangian description of i
rregular flows is equivalent to some class of random processes. (b) Fluid
flows correspond to the motion along a very non-regular set in a Hilbert s
pace. (c) The motion on such set can be described by the generalized D'Ale
mbert Principle which implies the energy dissipation even in the absence o
f friction (or viscosity). This statement is illustrated by simple model e
xamples. (d) The accurate formulation of the above principle requires the
use of the Nonstandard Analysis (NSA). (e) The above components imply the
existence of a weak solution for any initial velocity of finite energy.\nH
owever\, the study of the properties of those solutions requires further w
ork.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Sperone (Department of Mathematical Analysis\, Faculty o
f Mathematics and Physics\, Charles University in Prague)
DTSTART;VALUE=DATE-TIME:20201217T130000Z
DTEND;VALUE=DATE-TIME:20201217T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/6
DESCRIPTION:Title: Explicit bounds for the generation of a lift force exerted
by steady-state Navier-Stokes flows over a fixed obstacle\nby Gianmar
co Sperone (Department of Mathematical Analysis\, Faculty of Mathematics a
nd Physics\, Charles University in Prague) as part of Fudan International
Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe analyze
the steady motion of a viscous incompressible fluid\nin a two- and three-
dimensional channel containing an obstacle through\nthe Navier-Stokes equa
tions under different types of boundary\nconditions. In the 2D case we tak
e constant non-homogeneous Dirichlet\nboundary data in a (virtual) square
containing the obstacle\, and\nemphasize the connection between the appear
ance of lift and the unique\nsolvability of Navier-Stokes equations. In th
e 3D case we consider mixed\nboundary conditions: the inflow is given by a
fairly general datum and\nthe flow is assumed to satisfy a constant tract
ion boundary condition on\nthe outlet. In the absence of external forcing\
, explicit bounds on the\ninflow velocity guaranteeing existence and uniqu
eness of such steady\nmotion are provided after estimating some Sobolev em
bedding constants\nand constructing a suitable solenoidal extension of the
inlet velocity.\nIn the 3D case\, this solenoidal extension is built thro
ugh the Bogovskii\noperator and explicit bounds on its Dirichlet norm (in
terms of the\ngeometric parameters of the obstacle) are found by solving a
variational\nproblem involving the infinity-Laplacian.\nThe talk accounts
for results obtained in collaboration with Filippo\nGazzola and Ilaria Fr
agalà (both at Politecnico di Milano).\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Shibata (Waseda University\, Tokyo\, Japan)
DTSTART;VALUE=DATE-TIME:20210114T130000Z
DTEND;VALUE=DATE-TIME:20210114T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/7
DESCRIPTION:Title: R-bounded solution operators and mathematical fluid dynami
cs\nby Yoshihiro Shibata (Waseda University\, Tokyo\, Japan) as part o
f Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n
\nAbstract\nI would like to explain a systematic method of obtaining the m
aximal regularity\nof solutions for a system of a linear parabolic equatio
ns with non-homogeneous \nboundary conditions based on R-solution operator
s for the resolvent problem\nwith non-homogeneous boundary conditions. In
fact\, combination of \nR-bounded solution operators with the Weis opera
tor\nvalued Fourier multiplier theorem and extension of de Leeuv transfere
nce theorem\nto the operator valued Fourier multiplier yield the maximal r
egularity theorem\nfor the initial boundary value problem for linear parab
olic systems with non-homogeneous\nboundary conditions and high frequency
part of periodic solutions for linear\nparabolic system with non-homogeneo
us boundary conditions. \n\nAs application of our approach based on R-boun
ded solution operators\,\nI discuss the local and global well posedness o
f a free boundary problem for the Navier-Stokes equations in an exterior d
omain\, and the unique existence theorem of periodic solutions of\nthe Nav
ier-Stokes equations in a periodically moving three dimensional domain.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Reinhard Farwig (TU Darmstadt\, Germany)
DTSTART;VALUE=DATE-TIME:20210121T130000Z
DTEND;VALUE=DATE-TIME:20210121T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/8
DESCRIPTION:Title: The Navier-Stokes Equations in Bounded Domains with Moving
Boundaries\nby Professor Reinhard Farwig (TU Darmstadt\, Germany) as
part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechani
cs\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Paolo Maremonti (Università della Campania Luigi Vanvit
elli\, Caserta\, Italy)
DTSTART;VALUE=DATE-TIME:20210218T130000Z
DTEND;VALUE=DATE-TIME:20210218T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/9
DESCRIPTION:Title: On the uniqueness of a suitable weak solution to the Navie
r-Stokes Cauchy problem\nby Professor Paolo Maremonti (Università del
la Campania Luigi Vanvitelli\, Caserta\, Italy) as part of Fudan Internati
onal Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe ar
e dealing with the Navier-Stokes Cauchy problem. We investigate some resul
ts of regularity and uniqueness related to suitable weak solutions. The su
itable weak solution notion is meant in the sense introduced by Caffarelli
-Kohn-Nirenberg. In paper [1]\, we recognize that a suitable weak solution
enjoys more regularity than Leray-Hopf weak solutions\, that allows us to
furnish new uniqueness results for the solutions. Actually\, we realize t
wo results. The first one is a new sufficient condition on the initial dat
um u0 for uniqueness. We work on existing suitable weak solution\, that is
\, we do not construct a more regular weak solution corresponding to our i
nitial datum. The second result employs a weaker condition with respect to
previous ones (almost u0 is in L2)\, but\, just for one of the two compar
ed weak solutions\, we need a “special" Prodi-Serrin condition. It is
“special" as it is local in space.\n\nReferences\n\n[1] Crispo F. and Ma
remonti P.\, On the uniqueness of a suitable weak solution to the Navier-S
tokes Cauchy problem\, SN Partial Di_erential Equations and Applications\,
to appear.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Kristensen (University of Oxford)
DTSTART;VALUE=DATE-TIME:20210225T130000Z
DTEND;VALUE=DATE-TIME:20210225T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/10
DESCRIPTION:Title: Garding inequalities and their impact on regularity and u
niqueness\nby Jan Kristensen (University of Oxford) as part of Fudan I
nternational Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstrac
t\nMinimizers of strongly quasiconvex variational integrals need not be re
gular nor unique.\nHowever\, if a suitable G{\\aa}rding type inequality is
assumed for the variational integral\, then both regularity and uniquenes
s of minimizers can be restored under natural smallness conditions on the
data. In turn\, the G{\\aa}rding inequality turns out to always hold under
an a priori C1 regularity hypothesis on the minimizer\, while its validit
y is not known in the\ngeneral case. In this talk\, we discuss these issue
s and how they are naturally connected to convexity of the variational int
egral on the underlying Dirichlet classes.\n\nThe talk is based on joint w
ork with Judith Campos Cordero\, Bernd Kirchheim and Jan Kolar.\n\nThe Pas
scode to the recorded video is: \nUcH03YU!\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Agostina Vivaldi (SAPIENZA” UNIVERSITA DI ROMA)
DTSTART;VALUE=DATE-TIME:20210304T130000Z
DTEND;VALUE=DATE-TIME:20210304T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/11
DESCRIPTION:Title: SAND PILES MODELS AND NON-LINEAR DIFFUSION EQUATIONS\
nby Maria Agostina Vivaldi (SAPIENZA” UNIVERSITA DI ROMA) as part of F
udan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nA
bstract\nIn this talk\, we deal with theoretical and numerical aspects of
evolution and\ntime behavior of solutions to nonlinear diffusion equations
describing the dynamics of\nself-organizing sandpile process with the cri
tical state.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Hideo Kozono (Waseda University\, Tokyo)
DTSTART;VALUE=DATE-TIME:20210311T130000Z
DTEND;VALUE=DATE-TIME:20210311T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/12
DESCRIPTION:Title: Lr-Helmholtz-Weyl decomposition in two dimensional exteri
or domains\nby Professor Hideo Kozono (Waseda University\, Tokyo) as p
art of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanic
s\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Andrea Cianchi (University of Florence)
DTSTART;VALUE=DATE-TIME:20210318T130000Z
DTEND;VALUE=DATE-TIME:20210318T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/13
DESCRIPTION:Title: Symmetric gradient Orlicz-Sobolev spaces\nby Professo
r Andrea Cianchi (University of Florence) as part of Fudan International S
eminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nA unified a
pproach to embedding theorems for Sobolev type spaces of vector-valued fun
ctions\, defined via their symmetric gradient\, is proposed. The Sobolev s
paces in question are built upon general rearrangement-invariant norms. Op
timal target spaces in the relevant embeddings are determined within the c
lass of all rearrangement-invariant spaces. In particular\, all symmetric
gradient Sobolev embeddings into rearrangement-invariant target spaces are
shown to be equivalent to the corresponding embeddings for the full gradi
ent built upon the same spaces. A sharp condition for embeddings into spac
es of uniformly continuous functions\, and their optimal targets\, are als
o exhibited. By contrast\, these embeddings may be weaker than the corresp
onding ones for the full gradient. Related results\, of independent intere
st in the theory of symmetric gradient Sobolev spaces\, are established. T
hey include global approximation and extension theorems under minimal assu
mptions on the domain. A formula for the K-functional\, which is pivotal f
or our method based on a reduction to one-dimensional inequalities\, is pr
ovided as well. The case of symmetric gradient Orlicz-Sobolev spaces\, of
use in mathematical models in continuum mechanics driven by nonlinearities
of non-power type\, is especially focused. This is joint work with Domini
c Breit.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics
of Siberian Branch of the Russian Academy of Sciences\, Novosibirsk\, Russ
ia)
DTSTART;VALUE=DATE-TIME:20210408T130000Z
DTEND;VALUE=DATE-TIME:20210408T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/14
DESCRIPTION:Title: Concentrations and singularities of solutions to the Navi
er-Stokes equations of compressible isentropic flows\nby Professor Pa
vel Plotnikov (Lavrentyev Institute of Hydrodynamics of Siberian Branch of
the Russian Academy of Sciences\, Novosibirsk\, Russia) as part of Fudan
International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstra
ct\nAbstract. The talk is devoted to the theory of weak solutions to compr
essible Navier-Stokes equation with critical and subcritical adiabatic con
stants. In 2001\, Feireisl\, Novotny\, and Petzeltova proved the existence
of globally defined weak solutions to the Navier-Stokes equations of comp
ressible isentropic flows in the three space dimension on condition that t
he adiabatic constant is greater than critical value 3/2. The critical a
nd subcritical cases are still poor investigated. The main difficulty lies
in the fact that in the critical and subcritical cases\, the finite energ
y can be concentrated on sets of arbitrarily small measure. This leads to
the so-called concentration problem. In the present work\, we prove the ab
sence of concentrations of the kinetic energy tensor in the critical case.
We also give the derivation of estimates of non-stationary potentials of
the pressure function. These estimates allow us to estimate from below the
Hausdorff dimension of the support of the concentrations-defect measure.
The case of rotationally symmetric solutions with adiabaticconstant equal
s 1 is studied in details. In this case we prove that the concentrations-d
efect measure of the kinetic energy tensor is a matrix-valued measure\, wh
ich is concentrated on the symmetry axis and depends only on the time vari
able. In particular\, the divergence of the concentrations-defect measure
equals zero.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Neustupa (nstitute of Mathematics\, The Czech Academy of Scie
nces\, Prague\, Czech Republic)
DTSTART;VALUE=DATE-TIME:20210415T130000Z
DTEND;VALUE=DATE-TIME:20210415T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/15
DESCRIPTION:Title: New regularity criteria for weak solutions to the MHD equ
ations in terms of an associated pressure\nby Jiri Neustupa (nstitute
of Mathematics\, The Czech Academy of Sciences\, Prague\, Czech Republic)
as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mech
anics\n\n\nAbstract\nAssume that Omega is either a smooth bounded domain i
n R3 or Omega=R3\, and Omega' is a sub-domain of Omega. Our main theorem s
tates that if 0 <= T1 < T2 <= T <= \\infty\, (u\,b\,p) is a suitable weak
solution of an initial-boundary value problem for the MHD equations in Ome
ga x (0\,T)\, and either p- (the negative part of p) or B+ (the positive p
art of B:=p+|u|^2+|b|^2) satisfy certain new a posteriori conditions in Om
ega' x (T1\,T2) then the solution has no singular points in Omega' x (T1\,
T2). If b=0 then our theorem generalizes some known results from the theor
y of the Navier-Stokes equations. We give a comparison with previous relat
ed results and show the principles of the proof. The talk is based on a jo
int paper with Minsuk Yang\, Yonsei University\, Seoul.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Toshiaki Hishida (Nagoya University\, Japan)
DTSTART;VALUE=DATE-TIME:20210422T130000Z
DTEND;VALUE=DATE-TIME:20210422T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/16
DESCRIPTION:Title: Optimal boundary control for steady motions of a self-pro
pelled body in a viscous incompressible fluid\nby Professor Toshiaki H
ishida (Nagoya University\, Japan) as part of Fudan International Seminar
on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nConsider steady mo
tions of a self-propelled rigid body into an infinite viscous incompressib
le fluid in 3D. We say that a body undergoes a self-propelled motion if th
e external force and external torque acting on fluid-body are zero so that
the body moves only by a mechanism produced by itself at the boundary thr
ough fluid-body interaction. Given translational and angular velocities be
ing assumed to be small\, we show the existence of many boundary controls
subject to a physically relevant side condition (such as tangential contro
l or localized control) which generate the self-propelled motionof the bod
y with target velocity and then discuss minimizationof the work to overcom
e the drag. We next derive a necessary condition for optimal boundary cont
rol in terms of a variational inequality\, where the adjoint state associa
ted\nwith the optimal control is involved as a Lagrange multiplier. This t
alk is based on a joint work with Ana Silvestre (Lisbon) and Takeo Takahas
hi (Nancy).\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Antonin Novotny (University of Toulon\, IMATH\, France)
DTSTART;VALUE=DATE-TIME:20210429T130000Z
DTEND;VALUE=DATE-TIME:20210429T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/17
DESCRIPTION:Title: On the weak solvability of some compressible bi-fluid mod
els with general in/out-flow boundary data\nby Professor Antonin Novot
ny (University of Toulon\, IMATH\, France) as part of Fudan International
Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe will di
scuss the existence of weak solutions for some simple models of mixtures o
f several compressible viscous and noninteracting fluids. A particular att
ention in this talk will be devoted to the explanation of the role played
by the pure transport and continuity equations in the existence proof.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Eduard Feireisl (Institute of Mathematics of the Academy
of Sciences of the Czech Republic\; Institute of Mathematics\, Technische
Universitat Berlin)
DTSTART;VALUE=DATE-TIME:20210506T130000Z
DTEND;VALUE=DATE-TIME:20210506T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/18
DESCRIPTION:Title: Obstacle problem\, Euler system\, and turbulence\nby
Professor Eduard Feireisl (Institute of Mathematics of the Academy of Scie
nces of the Czech Republic\; Institute of Mathematics\, Technische Univers
itat Berlin) as part of Fudan International Seminar on Analysis\, PDEs\, a
nd Fluid mechanics\n\n\nAbstract\nWe consider a statistical limit of solut
ions to the compressible Navier-Stokes system in the high Reynolds number
regime in a domain exterior to a rigid body. We investigate to what extent
this highly turbulent regime can be modeled by an external stochastic per
turbation\, as suggested in the related physics literature.\nTo this end\,
we interpret the statistical limit as a stochastic process on the associa
ted trajectory space. We suppose that the limit process is statistically e
quivalent to a solution of the stochastic compressible Euler system. Then\
, necessarily\,\n(a) the stochastic forcing is not active - the limit is a
statistical solution of the deterministic Euler system\;\n(b) the solutio
ns S-converge to the limit\;\n(c) if\, in addition\, the expected value of
the limit process solves the Euler system\, then the limit is determinist
ic and the convergence is strong in the L^p-sense.\n \nThese results stron
gly indicate that a stochastic forcing may not be a suitable model for tur
bulent randomness in compressible fluid flows.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao Ren (Fudan University)
DTSTART;VALUE=DATE-TIME:20210513T130000Z
DTEND;VALUE=DATE-TIME:20210513T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/19
DESCRIPTION:Title: Leray's plane stationary solutions have the prescribed li
mit at infinity in the case of small Reynolds numbers\nby Xiao Ren (Fu
dan University) as part of Fudan International Seminar on Analysis\, PDEs\
, and Fluid mechanics\n\n\nAbstract\nIn the celebrated 1933 paper\, J. Ler
ay proposed the invading domains method to construct D-solutions for the s
tationary Navier-Stokes flow around obstacle problem. In two dimensions\,
whether Leray's D-solution achieves the prescribed limiting velocity at sp
atial infinity became a major open problem since then. In this paper\, we
solve this problem at small Reynolds numbers. The proof builds on a novel
blow-down argument which rescales the invading domains to the unit disc\,
and the ideas developed in a recent paper [Korobkov-Pileckas-Russo2020]\,
where the nontriviality of Leray solutions in the general case was proved\
, and [Korobkov-Ren-2021]\, where the uniqueness result for small Reynolds
number was established. The talk is based on a joint work with M.Korobkov
\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Guillod (Sorbonne University (France))
DTSTART;VALUE=DATE-TIME:20210520T130000Z
DTEND;VALUE=DATE-TIME:20210520T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/20
DESCRIPTION:Title: Stationary Navier–Stokes equations in the plane\nby
Julien Guillod (Sorbonne University (France)) as part of Fudan Internatio
nal Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nThe ai
m of this talk is to review the current knowledge on the steady solutions
of the Navier–Stokes equations in the whole two-dimensional plane. This
case is more difficult than the three-dimensional space for some reasons t
hat will be discussed. In the first part\, I will discuss the construction
of weak solutions through topological methods\, and in the second part ho
w the scaling invariance can be used to construct perturbative solutions.
I will mainly focus on the open problems and introduce some numerical resu
lts and conjectures.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Yasunori Maekawa (Kyoto University)
DTSTART;VALUE=DATE-TIME:20210527T130000Z
DTEND;VALUE=DATE-TIME:20210527T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/21
DESCRIPTION:Title: Gevrey stability of Rayleigh boundary layer in the invisc
id limit\nby Professor Yasunori Maekawa (Kyoto University) as part of
Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\n
Abstract\nWe will show the Prandtl boundary layer expansion for the two-di
mensional Navier-Stokes flows around the Rayleigh boundary layer\, which v
erifies the stability of the formation of the boundary layer in the invisc
id limit with respect to the perturbations in the Gevrey 3/2 class.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Ping Zhang (Kyoto University)
DTSTART;VALUE=DATE-TIME:20210603T130000Z
DTEND;VALUE=DATE-TIME:20210603T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/22
DESCRIPTION:Title: Global existence and decay of solutions to Prandtl system
with small analytic and Gevrey data\nby Professor Ping Zhang (Kyoto U
niversity) as part of Fudan International Seminar on Analysis\, PDEs\, and
Fluid mechanics\n\n\nAbstract\nIn this talk\, we prove the global existen
ce and the large time decay estimate of solutions to the Prandtl system wi
th small initial data\, which is analytical in the tangential variable.\n\
nThe key ingredient used in the proof is to derive a sufficiently fast dec
ay-in-time estimate of some weighted analytic energy estimate to a quantit
y\, which consists of a linear combination of the tangential velocity with
its primitive one\, and which basically controls the evolution of the ana
lytical radius to the solutions. Our result can be viewed as a global-in-t
ime Cauchy-Kowalevsakya result for the Prandtl system with small analytica
l data\, which in particular improves the previous result in \\cite{IV16}
concerning the almost global well-posedness of the two-dimensional Prandtl
system. Finally\, I'll present our recent result concerning the global we
ll-posedness with small Gevrey data. This is partially joint work with N.
Liu\; M. Paicu\; C. Wang and Y. Wang.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Anvarbek Meirmanov (National Research University "Higher
School of Economics"\, Moscow\, Russia)
DTSTART;VALUE=DATE-TIME:20210325T130000Z
DTEND;VALUE=DATE-TIME:20210325T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/23
DESCRIPTION:Title: Mathematical models of oil reservoir\nby Professor An
varbek Meirmanov (National Research University "Higher School of Economics
"\, Moscow\, Russia) as part of Fudan International Seminar on Analysis\,
PDEs\, and Fluid mechanics\n\n\nAbstract\nThis report is devoted to mathem
atical models of displacement of oil by some suspension in rocks during oi
l production. Mathematical models of the oil reservoir are very important
from both theoretical and practical points of view. So far\, one of the mo
st popular such models is the Backley-Leverett model. (1) Probably\, the
next known model could be the Muskat problem. (2) Each of these models is
a phenomenological mathematical model. That is\, it describes the physical
process at the macroscopic level\, where the characteristic size of the d
omain under consideration is several meters. We discuss existing phenomeno
logical models of oil reservoir and suggest new exact mathematical models
based on ideas R. Barridge and J. Keller (3) and E. Sanchez-Palencia (4) (
mathematical modelling) and G. Nguetseng (5) (homogenization). Finally\, w
e illustrate our results with some numerical implementations for one-poros
ity geometries and compare obtained results for different mathematical mod
els.\n\n1. S.E. Buckley and M.C. Leverett\, 1942\, Mechanism of fluid
displacements in sands\, Transactions of the AIME\, v.146\, pp. 107-116.\
n2. M. Muskat\, Two fluid systems in porous media. The encroachment of
water into an oil sand\, Physics\, 5\, 1934.\n3. R. Barridge and J. K
eller\, Poroelasticity equations derived from microstructure\, J. Acoust.
Soc. Am.\, V. 70\, issue 4\, 1981.\n4. E. Sanchez-Palencia\, Non-homog
eneous media and vibration theory\, Lecture Notes in Phys.\, 127\, Springe
r-Verlag\, Berlin–New York\, 1980.\n5. G. Nguetseng\, A general conv
ergence result for a functional related to the theory of homogenization\,
SIAM J. Math. Anal.\, V. 20\, issue 3\, 1989\, 608 - 623.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Grigory Seregin (Oxford University and St. Petersburg Instit
ute of Mathematics)
DTSTART;VALUE=DATE-TIME:20211014T130000Z
DTEND;VALUE=DATE-TIME:20211014T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/24
DESCRIPTION:Title: A Slightly Supercritical Condition of Regularity of Axisy
mmetric Solutions to the Navier-Stokes Equations\nby Prof. Grigory Ser
egin (Oxford University and St. Petersburg Institute of Mathematics) as pa
rt of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics
\n\n\nAbstract\nIn the talk\, a new regularity condition for axisymmetric
solutions to the non-stationary 3D Navier-Stokes equations is discussed. I
t is slightly supercritical.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Yosef Yomdin (The Weizmann Institute of Science\, Rehovot\,
Israel)
DTSTART;VALUE=DATE-TIME:20211104T130000Z
DTEND;VALUE=DATE-TIME:20211104T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/26
DESCRIPTION:Title: Estimating high order derivatives of a function through g
eometry and topology of its zero set\nby Prof. Yosef Yomdin (The Weizm
ann Institute of Science\, Rehovot\, Israel) as part of Fudan Internationa
l Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe study
a very special setting of the Whitney smooth extension problem: for a giv
en closed subset Z in the ball B^n\, we consider normalized (d+1)-smooth f
unctions f on B^n\, vanishing on Z\, and ask for the minimal possible norm
||f^(d+1)|| of their last derivative. We discuss some recent results in
this direction\, which use as an input the ``density’’ of Z\, or\, in
contrast\, its topology. In particular\, the role of the density of Z is
analyzed via Remez-type inequalities\, on one side\, and via restriction t
o smooth curves\, on the other side.\n\n In order to incorporate topologic
al information on Z\, we use\, in particular\, some recent results of Lera
rio and Stecconi\, comparing topology of smooth transversal singularities\
, and of their polynomial approximations. If time allows\, we plan also to
present the lower bounds on the minimal possible norm ||f^(d+1)||\, given
the set of critical values of f.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Andrej Zlatos (University of California\, San Diego\, US
A)
DTSTART;VALUE=DATE-TIME:20211118T130000Z
DTEND;VALUE=DATE-TIME:20211118T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/27
DESCRIPTION:Title: Euler Equations on General Planar Domains\nby Profess
or Andrej Zlatos (University of California\, San Diego\, USA) as part of F
udan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nA
bstract\nBounded vorticity solutions to the 2D Euler equations on singular
domains are typically not close to Lipschitz near boundary singularities\
, which makes their uniqueness a difficult open problem. I will present a
general sufficient condition on the geometry of the domain that guarantees
global uniqueness for all solutions initially constant near the boundary.
This condition is only slightly more restrictive than exclusion of corner
s with angles greater than $\\pi$ and\, in particular\, is satisfied by al
l convex domains. Its proof is based on showing that fluid particle trajec
tories for general bounded vorticity solutions cannot reach the boundary i
n finite time. The condition also turns out to be sharp in the latter sens
e: there are domains that come arbitrarily close to satisfying it and on w
hich particle trajectories can reach the boundary in finite time.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Semyon Dyatlov (Massachusetts Institute of Technology\,
USA)
DTSTART;VALUE=DATE-TIME:20211216T130000Z
DTEND;VALUE=DATE-TIME:20211216T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/28
DESCRIPTION:Title: Quantum chaos: advances and perspectives\nby Professo
r Semyon Dyatlov (Massachusetts Institute of Technology\, USA) as part of
Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\n
Abstract\nWhere do eigenfunctions of the Laplacian concentrate as eigenval
ues go to infinity? Do they equidistribute or do they concentrate in an un
even way? It turns out that the answer depends on the nature of the geodes
ic flow. I will discuss various results in the case when the flow is chaot
ic: the Quantum Ergodicity theorem of Shnirelman\, Colin de Verdi\\`ere\,
and Zelditch\, the Quantum Unique Ergodicity conjecture of Rudnick--Sarnak
\, the progress on it by Lindenstrauss and Soundararajan\, and the entropy
bounds of Anantharaman--Nonnenmacher. I will conclude with a more recent
lower bound on the mass of eigenfunctions obtained with Jin and Nonnenmach
er. It relies on a new tool called "fractal uncertainty principle" develop
ed in the works with Bourgain and Zahl.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Igor Pazanin (University of Zagreb\, Croatia)
DTSTART;VALUE=DATE-TIME:20220113T130000Z
DTEND;VALUE=DATE-TIME:20220113T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/29
DESCRIPTION:Title: The effective boundary condition on a porous wall\nby
Professor Igor Pazanin (University of Zagreb\, Croatia) as part of Fudan
International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstra
ct\nThe aim of this talk is to present the derivation of the new effective
boundary condition for the fluid flow in a domain with porous boundary. S
tarting from the Stokes system in a domain with an array of small holes on
the boundary and using the homogenization and the boundary layers\, we fi
nd an effective law in the form of generalized Darcy law. If the pores geo
metry is isotropic\, then the condition splits in Beavers-Joseph type cond
ition for the tangential flow and the standard Darcy condition for the nor
mal flow. In the second part of the talk\, we study the roughness-induced
effects on the proposed Darcy-type boundary condition.\n\nThe talk is base
d on the joint work with Eduard Marusic-Paloka.\n\nPasscode for the Record
ed video link: c=q5RuW0\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Alexander Nazarov (St. Petersburg Department of Steklov
Institute of Mathematics (POMI) and St. Petersburg State University\, Rus
sia)
DTSTART;VALUE=DATE-TIME:20220127T130000Z
DTEND;VALUE=DATE-TIME:20220127T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/30
DESCRIPTION:Title: The Hopf-Oleinik Lemma for the divergence-type equations<
/a>\nby Professor Alexander Nazarov (St. Petersburg Department of Steklov
Institute of Mathematics (POMI) and St. Petersburg State University\, Rus
sia) as part of Fudan International Seminar on Analysis\, PDEs\, and Fluid
mechanics\n\n\nAbstract\nThe Hopf-Oleinik lemma\, known also as the “no
rmal derivative lemma”\, is one of the important tools in qualitative an
alysis of partial differential equations.This lemma states that a supersol
ution of a partial differential equation with a minimum value at a boundar
y point\, must increase linearly away from its boundary minimum provided t
he boundary is smooth enough. A major part of all known results on the nor
mal derivative lemma concerns equations with nondivergence structure and s
trong solutions (see [1] and [2] for some recent results and the comprehen
sive historical review). \n\n The case of the divergence-type equations is
less studied. It is well known that the normal derivative lemma fails for
uniformly elliptic equations in divergence form with bounded and even con
tinuous leading coefficients. Thus\, one has to require more smoothness of
the leading coefficients. \n\nFor the parabolic divergence-type equations
\, the normal derivative lemma can be also extracted from the lower bound
estimates of the Green function for the corresponding operator.\n\nWe pres
ent a version of the Hopf-Oleinik lemma for general elliptic and parabolic
equations in divergence form under the sharp requirements on the coeffici
ents of equations and on the boundary of a domain. All our assumptions are
significantly weakened in comparison with the previous works. In fact\, o
ur requirements are close to the necessary ones. The talk is based on the
paper [3]. \n\nReferences\n\n[1] A.I. Nazarov\, A centennial of the Zaremb
a-Hopf-Oleinik lemma\, SIAM J. Math. Anal. 44(2012)\, no. 1\, 437–453.\n
\n[2] D.E. Apushkinskaya\, A.I. Nazarov\, A counterexample to the Hopf-Ole
inik lemma (elliptic case)\, Anal. PDE 9(2016)\, no. 2\, 439–458.\n\n[3]
D.E. Apushkinskaya\, A.I. Nazarov\, On the Boundary Point Principle fordi
vergence-type equations\, Rend. Lincei Mat. Appl. 30(2019)\, 677–699.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao Ren (Fudan university\, Shanghai\, China)
DTSTART;VALUE=DATE-TIME:20220224T130000Z
DTEND;VALUE=DATE-TIME:20220224T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/31
DESCRIPTION:Title: Existence and uniqueness for plane stationary Navier–St
okes flows with compactly supported force\nby Xiao Ren (Fudan universi
ty\, Shanghai\, China) as part of Fudan International Seminar on Analysis\
, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe prove two basic estimates f
or 2D stationary Navier-Stokes solutions\, which have rather simple forms.
Then\, we apply them to the stationary Navier–Stokes equations in the w
hole plane with an external force and with a prescribed constant spatial l
imit. Using the first estimate\, we solve the key difficulties in applying
Leray’s invading domains method in the whole plane and\, as a consequen
ce\, prove the existence of stationary Navier-Stokes D-solutions with arbi
trary compactly supported force. Using the second estimate\, we verify the
boundary condition at infinity in two different scenarios: (I) the limit
velocity is sufficiently large with respect to the external force\, (II) b
oth the total integral of force and the limit velocity vanish. Hence\, our
method produces large class of new solutions with prescribed spatial limi
ts. We also show the uniqueness of D-solutions to the forced problem in a
perturbative regime. \nThe talk is based on the recent joint paper with Ju
lien Guillod (Sorbonne Universite) and Mikhail Korobkov\, see https://arxi
v.org/abs/2111.11042\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor David Gomes-Castro (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220310T130000Z
DTEND;VALUE=DATE-TIME:20220310T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/32
DESCRIPTION:Title: Concentration phenomena in Aggregation-Diffusion Equation
s\nby Professor David Gomes-Castro (University of Oxford) as part of
Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\nAb
stract: TBA\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Giovanni Paolo Galdi (University of Pittsburgh\, USA)
DTSTART;VALUE=DATE-TIME:20220324T130000Z
DTEND;VALUE=DATE-TIME:20220324T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/33
DESCRIPTION:Title: Navier-Stokes Equations around a Rigid Body: Three Remark
able Open Problems\nby Professor Giovanni Paolo Galdi (University of P
ittsburgh\, USA) as part of Fudan International Seminar on Analysis\, PDEs
\, and Fluid mechanics\n\n\nAbstract\nThe motion of a (finite) rigid body\
, B\, in a viscous liquid is a fundamental and widely investigated problem
of mathematical fluid mechanics\, in both cases when the motion of B is e
ither prescribed or it becomes part of the problem. However\, in spite of
the many outstanding contributions tracing back to the works of Leray\, La
dyzhenskaya and Finn\, there is still a plethora of fundamental questions
that remain still unanswered and call for the attention of the interested
mathematician. Objective of this talk is to present and discuss three amon
g the most remarkable ones.\n\nPasscode for the video-link: EeGU5+k7\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Timofey Shilkin (St.-Petersburg Branch of V.A. Steklov I
nstitute of Mathematics)
DTSTART;VALUE=DATE-TIME:20220407T130000Z
DTEND;VALUE=DATE-TIME:20220407T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/34
DESCRIPTION:Title: Surprising properties of weak solutions to elliptic equat
ions with a singular drift\nby Professor Timofey Shilkin (St.-Petersbu
rg Branch of V.A. Steklov Institute of Mathematics) as part of Fudan Inter
national Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nW
e study properties of weak solutions to the Dirichlet problem for scalar e
lliptic equations of the convection-diffusion type. It is well-known that
in the case of a regular drift (which is not necessarily divergence-free)
weak solutions possess a set of properties which are typical in the ellipt
ic theory. In this talk we will follow how the properties of weak solution
s change in the case when the drift has limited smoothness.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Dallas Albritton (Institute for Advanced Study\, USA)
DTSTART;VALUE=DATE-TIME:20220421T130000Z
DTEND;VALUE=DATE-TIME:20220421T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/35
DESCRIPTION:Title: Non-uniqueness of Leray solutions of the forced Navier-St
okes equations\nby Professor Dallas Albritton (Institute for Advanced
Study\, USA) as part of Fudan International Seminar on Analysis\, PDEs\, a
nd Fluid mechanics\n\n\nAbstract\nIn a seminal work\, Leray demonstrated t
he existence of global weak solutions to the Navier-Stokes equations in th
ree dimensions. Are Leray's solutions unique? This is a fundamental questi
on in mathematical hydrodynamics\, which we answer in the negative\, withi
n the `forced' category\, by exhibiting two distinct Leray solutions with
zero initial velocity and identical body force. This is joint work with El
ia Brué and Maria Colombo.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Filippo Gazzola (The Polytechnic University of Milan)
DTSTART;VALUE=DATE-TIME:20220428T130000Z
DTEND;VALUE=DATE-TIME:20220428T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/36
DESCRIPTION:Title: Long-time behavior of partially damped systems modeling d
egenerate plates with piers\nby Professor Filippo Gazzola (The Polytec
hnic University of Milan) as part of Fudan International Seminar on Analys
is\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe consider a partially dam
ped nonlinear beam-wave system of evolution PDE's modeling the dynamics of
a degenerate plate. The plate can move both vertically and torsionally an
d\, consequently\, the solution has two components. We show that the compo
nent from the damped beam equation always vanishes asymptotically while th
e component from the (undamped) wave equation does not. In case of small e
nergies we show that the first component vanishes at exponential rate. Our
results highlight that partial damping is not enough to steer the whole s
olution to rest and that the partially damped system can be less stable th
an the undamped system. Hence\, the model and the behavior of the solution
enter in the framework of the so-called "indirect damping" and "destabili
zation paradox". These phenomena are valorized by a physical interpretatio
n leading to possible new explanations of the Tacoma Narrows Bridge collap
se.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Tobias Barker (University of Bath\, UK)
DTSTART;VALUE=DATE-TIME:20220505T130000Z
DTEND;VALUE=DATE-TIME:20220505T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/37
DESCRIPTION:Title: Failure of Liouville type theorems and potential 'type I'
singularities of the Navier-Stokes equations\nby Professor Tobias Bar
ker (University of Bath\, UK) as part of Fudan International Seminar on An
alysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nIt is known that if a s
olution of the 3D Navier-Stokes equations loses smoothness\, then there ne
cessarily exists a non-zero bounded solution defined on the whole backward
time interval. \nIn this talk\, I will focus on the reverse implication.
\nJoint work with Dallas Albritton (IAS).\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Gisella Croce (Laboratoire de Mathematiques Appliquees d
u Havre)
DTSTART;VALUE=DATE-TIME:20220519T130000Z
DTEND;VALUE=DATE-TIME:20220519T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/38
DESCRIPTION:Title: On the quantitative isoperimetric inequality in the plane
\nby Professor Gisella Croce (Laboratoire de Mathematiques Appliquees
du Havre) as part of Fudan International Seminar on Analysis\, PDEs\, and
Fluid mechanics\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Anvar Meirmanov (Moscow State University of Civil Engine
ering\, Moscow)
DTSTART;VALUE=DATE-TIME:20220602T130000Z
DTEND;VALUE=DATE-TIME:20220602T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/39
DESCRIPTION:Title: On the classical solution to the macroscopic model for in
-situ leaching of rare metals\nby Professor Anvar Meirmanov (Moscow St
ate University of Civil Engineering\, Moscow) as part of Fudan Internation
al Seminar on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe cons
ider initial boundary value problems arising in mathematical models for in
-- situ leaching of rare metals or for cleaning the bottom-hole zone of o
il wells with\ndouble - porosity structure and special periodicity.\nFirst
\, we consider this physical process at the microscopic level (the charact
eristic pore size is approximately 5-20 microns\, governed by Lame equati
ons for the solid skeleton\, the Stokes equations for the liquid component
\, and the diffusion-convection equations for concentrations of acid and p
roducts of a chemical reaction. \nDue to its dissolution\, the solid skele
ton has an unknown (free) boundary with the pore and cavity spaces. \nNext
\, assuming the existence of a generalized solution to the corresponding i
nitial-boundary value problem at the microscopic level and using the homog
enization method together with the fixed point theorem\, we derive the Bio
's model describing the physical process of in-situ leaching for slightly
viscous liquid in the double - porosity elastic solid skeleton at the macr
oscopic level.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Piotr Hajłasz (University of Pittsburgh\, USA)
DTSTART;VALUE=DATE-TIME:20221020T130000Z
DTEND;VALUE=DATE-TIME:20221020T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/40
DESCRIPTION:Title: Approximation of mappings with derivatives of low rank\nby Professor Piotr Hajłasz (University of Pittsburgh\, USA) as part of
Fudan International Seminar on Analysis\, PDEs\, and Fluid mechanics\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Stefano Modena (Gran Sasso Science Institute (GSSI)\, It
aly)
DTSTART;VALUE=DATE-TIME:20221103T130000Z
DTEND;VALUE=DATE-TIME:20221103T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/41
DESCRIPTION:Title: Non-uniqueness for the transport equation with Sobolev ve
ctor fields\nby Professor Stefano Modena (Gran Sasso Science Institute
(GSSI)\, Italy) as part of Fudan International Seminar on Analysis\, PDEs
\, and Fluid mechanics\n\n\nAbstract\nOne of the main questions in the the
ory of the linear transport equation is whether uniqueness of weak solutio
ns to the Cauchy problem holds in the case the given vector field is not s
mooth. In the talk I will provide an overview on some results obtained in
the last few years\, showing that even for incompressible\, Sobolev (thus
quite ``well-behaved") vector fields\, uniqueness of solutions can drastic
ally fail. This result can be seen as a counterpart to DiPerna and Lions'
well-posedness theorem.\n\nPasscode for the video-link:S*9@4C#H\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics\,
Novosibirsk)
DTSTART;VALUE=DATE-TIME:20221117T130000Z
DTEND;VALUE=DATE-TIME:20221117T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/42
DESCRIPTION:Title: Isothermal coordinates on surfaces with a square-integrab
le second fundamental form. Existence and counterexamples\nby Professo
r Pavel Plotnikov (Lavrentyev Institute of Hydrodynamics\, Novosibirsk) as
part of Fudan International Seminar on Analysis\, PDEs\, and Fluid mechan
ics\n\n\nAbstract\nThe question of the existence of isothermal coordinates
on two-dimensional surfaces goes back to the work of Gauss on differentia
l geometry. The first nonlocal theorem on the existence of isothermal coor
dinates for quadratic differential forms with smooth coefficients was prov
ed by Lichtenstein (1916). For forms with bounded coefficients this result
was established by Morrey(1938). Morrey's theorem has been repeatedly rep
roved and refined. In modern literature\, it is often referred to as the A
hlfors-Bers-Bojarski-Morrey theorem. Here we should also mention the resul
t of Helein (2002) on the existence isothermal coordinates for differentia
l quadratic forms with Sobolev coefficients.\n For many applications\,
it is important to find isothermal coordinates with a uniformly bounded co
nformal factor logarithm. Such coordinates are called bi-Lipschitz coordin
ates. The existence of bi-Lipschitz coordinates is an essential ingredient
of the mathematical theory of biological membranes. In 1994 Toro proved
the remarkable theorem on the existence of bi-Lipschitz isothermal coordin
ates for surfaces with a square-integrable second fundamental form. It sh
ould be noted that her approach is based on the theory of varifolds and ge
ometric measure theory. An analytical approach to the problem was proposed
in the works of Kuwert and Li\, and Riviera (2012). They introduced a cl
ass of weak immersions with a square-integrable second fundamental form. A
n immersion of a two-dimensional closed manifold into a Euclidean space be
longs to this class if its first fundamental form is uniformly bounded abo
ve and below\, and its second fundamental form is square integrable.\n
A common belief is the existence of bi-Lipschitz isothermal coordinates f
or all such immersions. This fact is widely used in the mathematical theor
y of biological membranes. In the proposed work\, we show that this assert
ion is not true in the general case. We give an example of weak immersion
of a two-dimensional sphere for which there are no bi-Lipschitz isothermal
coordinates. On the other hand\, we prove the existence of such coordinat
es for all weak immersions of tori. The connection of these results with T
eichmüller's theory is discussed. Our approach is based on the Chern-Hele
in moving frame method and the Moser-Struwe result on the validity of the
Liouville theorem for elliptic equations with bounded periodic coefficient
s.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Eduard Marušić-Paloka (University of Zagreb\, Croatia)
DTSTART;VALUE=DATE-TIME:20221201T130000Z
DTEND;VALUE=DATE-TIME:20221201T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/43
DESCRIPTION:Title: Mathematical model of heat transfer through a conductive
pipe\nby Professor Eduard Marušić-Paloka (University of Zagreb\, Cro
atia) as part of Fudan International Seminar on Analysis\, PDEs\, and Flui
d mechanics\n\n\nAbstract\nThe standard engineer's model for heat transfer
between the fluid flowing through the pipe and the exterior medium neglec
ts the effects of the pipe's wall. The goal of this paper is to prove that
they are not always negligible. Comparing the ratio between diffusivities
of the fluid and the wall with the wall's thickness\, using rigorous asym
ptotic analysis\, we find five different models for effective description
of the heat exchange process.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Piotr B Mucha (University of Warsaw\, Poland)
DTSTART;VALUE=DATE-TIME:20221215T130000Z
DTEND;VALUE=DATE-TIME:20221215T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/44
DESCRIPTION:Title: A new construction of weak solutions to compressible Navi
er-Stokes equations\nby Professor Piotr B Mucha (University of Warsaw\
, Poland) as part of Fudan International Seminar on Analysis\, PDEs\, and
Fluid mechanics\n\n\nAbstract\nI plan to talk about the existence of the w
eak solutions to the compressible Navier--Stokes system with barotropic pr
essure for $\\gamma \\geq 9/5$ in three dimension. The novelty of the pape
r is the approximation scheme that instead of the classical regularization
of the continuity equation (based on the viscosity approximation $\\epsil
on \\Delta$) uses more direct truncation and regularisation of nonlinear
terms an the pressure. This scheme is compatible with the Bresch-Jabin co
mpactness criterion for the density. We revisit this criterion and prove\
, in full rigour\, that it can be applied in our approximation at any leve
l.\n\nBased on: Nilasis Chaudhuri\, Piotr B. Mucha\, Ewelina Zatorska -- a
rXiv:2211.12189\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Professor Patrick Tolksdorf (Johannes Gutenberg-Universität Mainz
\, Germany)
DTSTART;VALUE=DATE-TIME:20230105T130000Z
DTEND;VALUE=DATE-TIME:20230105T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/45
DESCRIPTION:Title: L^p-extrapolation of the generalized Stokes operator\
nby Professor Patrick Tolksdorf (Johannes Gutenberg-Universität Mainz\, G
ermany) as part of Fudan International Seminar on Analysis\, PDEs\, and Fl
uid mechanics\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:professor Reinhard Farwig (Technische Universität Darmstadt\, Dar
mstadt\, Germany)
DTSTART;VALUE=DATE-TIME:20230119T130000Z
DTEND;VALUE=DATE-TIME:20230119T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/46
DESCRIPTION:Title: The Navier-Stokes System with Moving Boundaries - From Bo
unded to Unbounded Domains\nby professor Reinhard Farwig (Technische U
niversität Darmstadt\, Darmstadt\, Germany) as part of Fudan Internationa
l Seminar on Analysis\, PDEs\, and Fluid mechanics\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:professor Vincenzo Ferone (Università degli Studi di Napoli Feder
ico II\, Naples\, Italy)
DTSTART;VALUE=DATE-TIME:20230223T130000Z
DTEND;VALUE=DATE-TIME:20230223T140000Z
DTSTAMP;VALUE=DATE-TIME:20230331T095701Z
UID:Cafe_Analysis_and_Fluid/47
DESCRIPTION:Title: Symmetrization for linear and nonlinear fractional ellipt
ic problems\nby professor Vincenzo Ferone (Università degli Studi di
Napoli Federico II\, Naples\, Italy) as part of Fudan International Semina
r on Analysis\, PDEs\, and Fluid mechanics\n\n\nAbstract\nWe describe symm
etrization results in the form of mass concentration (i.e. integral) compa
rison for fractional elliptic equations involving the s-laplacian (0 < s <
1). We use a new direct method which recovers\, in the limit as s goes to
1\, the classical pointwise Talenti rearrangement inequality. Some possib
le applications of the method to nonlinear equations and to equations with
lower order terms will be discussed.\n
LOCATION:https://researchseminars.org/talk/Cafe_Analysis_and_Fluid/47/
END:VEVENT
END:VCALENDAR