We show that weak solutions of degenerate Navier-Stokes equati ons converge\nto the strong solutions of the pressureless Euler system wit h linear drag term\, Newtonian\nrepulsion and quadratic confinement. The p roof is based on the relative entropy method\nusing the artificial velocit y formulation for the one-dimensional Navier-Stokes system.\n
\n\nTh e result is based on the joint work with Jose A. Carrillo and Ewelina Zato rska.
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Vasseur (University of Texas at Austin) DTSTART:20201123T170000Z DTEND:20201123T172000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/6 DESCRIPTION:Title: Instability of finite time blow-ups for incompressible Euler\nby Alexis Vasseur (University of Texas at Austin) as part of BIRS workshop: M ultiscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\nIn this talk\, we will discuss the interaction between the stability\, and the propagation of regularity\, for solutions to the incompressible 3D Euler equation. It is still unknown whether a solution with smooth initia l data can develop a singularity in finite time. We will explain why the p rediction of such a blow-up\, via direct numerical experiments\, is so dif ficult. We will describe how\, in such a scenario\, the solution becomes u nstable as time approaches the blow-up time. The method use the relation b etween the vorticity of the solution\, and the bi-characteristic amplitude solutions\, which describe the evolution of the linearized Euler equation at high frequency. In the axisymmetric case\, we can also study the insta bility of blow-up profiles. \n
\nThis work was partially supported b y the NSFDMS-1907981. \n
\nThis a joint work with Misha Vishik and L aurent Lafleche.
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ondřej Kreml (Czech Academy of Sciences) DTSTART:20201123T172500Z DTEND:20201123T174500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/7 DESCRIPTION:Title: Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data\nby Ondřej Kreml (Czech Academy o f Sciences) as part of BIRS workshop: Multiscale Models for Complex Fluids : Modeling and Analysis\n\n\nAbstract\nWe consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a $C^\\infty$ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation betwe en smooth solutions to the Euler system and to the Burgers equation we con struct a smooth compression wave which collapses into a perturbed Riemann state at some time instant $T > 0$. In order to continue the solution afte r the formation of the discontinuity\, we adjust and apply the theory deve loped by De Lellis and Székelyhidi and we construct infinitely many solut ions.\n
\n\nThis is a joint work with Elisabetta Chiodaroli\, V\\'ac lav M\\'acha and Sebastian Schwarzacher. \n
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Renardy (Virginia Tech) DTSTART:20201123T175000Z DTEND:20201123T182000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/8 DESCRIPTION:Title: Pure stress modes for linear viscoelastic flows with variable coeffic ients\nby Michael Renardy (Virginia Tech) as part of BIRS workshop: Mu ltiscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\n< p>We consider the equations of a linear Maxwell fluid with spatially varyi ng coefficients. Pure stress modes are solutions with zero velocity but no nzero stresses. We derive equations to characterize such solutions. In two dimensions\, we find that under generic hypotheses only certain "trivial" solutions exist. In three dimensions\, on the other hand\, there exist no ntrivial solutions. To get them\, we derive a system of partial differenti al equations whose type (elliptic or hyperbolic) depends on the sign of th e Gauss curvature of level surfaces of the relaxation time. \n\n\n\ n(joint work with Debanjana Mitra and Mythily Ramaswamy)\n
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomas Barta (Charles University) DTSTART:20201124T130000Z DTEND:20201124T132000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/9 DESCRIPTION:Title: Decay of solutions to integrodifferential equations\nby Tomas Bar ta (Charles University) as part of BIRS workshop: Multiscale Models for Co mplex Fluids: Modeling and Analysis\n\n\nAbstract\nWe discuss long time be havior of solutions to a non-linear second order integrodifferential convo lution equation\, in particular we focus on the speed of convergence to eq uilibrium. The key assumptions are that the convolution kernel is small an d the non-linear operator satisfies the Lojasiewicz inequality.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Dostalik (Charles University) DTSTART:20201124T132500Z DTEND:20201124T134500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/10 DESCRIPTION:Title: Thermodynamically consistent derivation of a micro-macro model for d ilute polymeric fluids\nby Mark Dostalik (Charles University) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analy sis\n\n\nAbstract\nThe rheology of complex fluids such as polymeric liquid s is highly non-Newtonian in nature and manifests itself as an extra stres s component in the Cauchy stress tensor. At the purely macroscopic level\, the extra stress tensor is linked to the velocity field through\, say\, a partial differential equation. An alternative approach consists in findin g an expression for the macroscopic extra stress tensor in terms of the mi croscopic dynamics of the polymer chains. We present a thermodynamically b ased approach to the design of a class of such micro-macro models for dilu te polymeric liquids and show that the thermodynamic background of the mod el naturally yields stability of the steady state when the fluid occupies an isolated vessel.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Mucha (University of Warsaw) DTSTART:20201124T135000Z DTEND:20201124T141000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/11 DESCRIPTION:Title: Flows initiated by ripped density\nby Piotr Mucha (University of Warsaw) as part of BIRS workshop: Multiscale Models for Complex Fluids: M odeling and Analysis\n\n\nAbstract\nInstead of the abstract\, please see t he video on https://youtu.be/l85eQa pJ_bA.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Dalibor Pražák (Charles University) DTSTART:20201124T150000Z DTEND:20201124T152000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/12 DESCRIPTION:Title: A finite-dimensional reduction of dissipative dynamical systems\ nby Dalibor Pražák (Charles University) as part of BIRS workshop: Multis cale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\nWe show that under natural regularity assumptions\, an abstract nonlinear pa rabolic evolution problem has a finite-dimensional attractor. Moreover\, t he long-time dynamics can be recast as a system of ODEs with exponentially decaying delay.\n
\n\nAs an application\, we consider a class of no n-Newtonian fluids with dynamic boundary conditions.\n
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Woznicki (University of Warsaw) DTSTART:20201124T152500Z DTEND:20201124T154500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/13 DESCRIPTION:Title: Mv-strong uniqueness for density dependent\, incompressible\, non-Ne wtonian fluids\nby Jakub Woznicki (University of Warsaw) as part of BI RS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n \n\nAbstract\n\nWe analyse the system of the form\n\\begin{align*}\n {\\partial}_t{\\rho} +{\\rm div \\\,}_x(\\rho u) = 0\\\\\n {\\partial}_ t(\\rho u) +{\\rm div \\\,}_x(\\rho u\\otimes u) + \\nabla_x p = {\\rm div \\\,}_x {\\mathbb{S}}\\label{secondequation}\\\\\n {\\rm div \\\,}_x(u ) = 0\n\\end{align*}\nwhere $\\rho$ is the mass density\, $u$ denotes velo city field\, ${\\mathbb{S}}$ the stress tensor and $p$ is the pressure. We are interested in the measure-valued solutions to those equations and pro ve the mv-strong uniqueness property. This work bases its assumptions on t he recent paper by Abbatiello and Feireisl [1]\, but differs from it in de nsity dependency. Surprisingly the solutions are not defined by the Young measures\, but by the similar tool to the so-called defect measure.\n
\ n\n\n
\nIn multiscale models for polymeric fluids\, the evolution of the polymer chain is usual ly modeled using an entropic force\, computed from the free energy associa ted with the end-to-end vector. We will present results which aim at justi fying under which circumstances such a dynamics is indeed close to the ori ginal dynamics based on the full-atom chain.\n
\n\nClassical models describing the motion of Newtonian fluids\ , such as water\, rely on the assumption that the Cauchy stress is a linea r function of the symmetric part of the velocity gradient of the fluid. Th is assumption leads to the Navier-Stokes equations. It is known however th at the framework of classical continuum mechanics\, built upon an explicit constitutive equation for the Cauchy stress\, is too narrow to describe i nelastic behavior of solid-like materials or viscoelastic properties of ma terials. Our starting point in this work is therefore a generalization of the classical framework of continuum mechanics\, called the implicit const itutive theory\, which was proposed recently in a series of papers by K.R. Rajagopal. The underlying principle of implicit constitutive theory in th e context of viscous flows is the following: instead of demanding that the Cauchy stress is an explicit (and\, in particular\, linear) function of t he symmetric part of the velocity gradient\, one may allow a nonlinear\, i mplicit and not necessarily continuous relationship between these quantiti es. The resulting general theory therefore admits non-Newtonian fluid flow models with implicit and possibly discontinuous power-law-like rheology.\ n
\n\nWe develop the analysis of finite element approximations of im plicit power-law-like models for viscous in-compressible fluids. The Cauch y stress and the symmetric part of the velocity gradient in the class of m odels under consideration are related by a\, possibly multi-valued\, maxim al monotone graph. Using a variety of weak compactness techniques\, we sho w that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the discretisation parameter\, measu ring the granularity of the finite element triangulation\, tends to zero. A key new technical tool in our analysis is a finite element counterpart o f the Acerbi-Fusco Lipschitz truncation of Sobolev functions.\n
\n\n The talk is based on a series of recent papers with Lars Diening and Tabea Tscherpel (Bielefeld)\, Christian Kreuzer (Dortmund)\, Alexei Gazca Orozc o (Erlangen) and Patrick Farrell (Oxford).\n
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Vít Průša (Charles University) DTSTART:20201124T175000Z DTEND:20201124T181000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/17 DESCRIPTION:Title: Thermodynamics of viscoelastic rate-type fluids and its implications for stability analysis\nby Vít Průša (Charles University) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analy sis\n\n\nAbstract\nAnalysis of finite amplitude stability of fluid flows i s a challenging task even if the fluid of interest is described using the classical mathematical models such as the Navier--Stokes--Fourier model. T he issue gets more complicated when one has to deal with complex models fo r coupled thermomechanical behaviour of non-Newtonian fluids\; in particul ar the viscoelastic rate-type fluids.\nWe consider the barotropic Navier-Stokes system describing the motion of a compressible viscous fluid confined to a bounded domain driven by ti me periodic inflow/outflow boundary conditions. We show that the problem a dmits a time-periodic solution in the class of weak solutions satisfying t he energy inequality. \n
\n\nThis is a joint work with Eduard Feirei sl.
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Ewelina Zatorska (University College London) DTSTART:20201125T132500Z DTEND:20201125T134500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/19 DESCRIPTION:Title: On the dynamical network of interacting particles: from micro to mac ro\nby Ewelina Zatorska (University College London) as part of BIRS wo rkshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n\n\nA bstract\nIn this talk I will present a derivation of macroscopic model of interacting particles. The population of N particles evolve according to a diffusion process and interacts through a dynamical network. In turn\, th e evolution of the network is coupled to the particles' positions. In con trast with the mean-field regime\, in which each particle interacts with e very other particle\, i.e. with O(N) particles\, we consider the a priori more difficult case of a sparse network\; that is\, each particle interac ts\, on average\, with O(1) particles. We also assume that the network' s dynamics is much faster than the particles' dynamics. The derivation co mbines the stochastic averaging (over time-scale parameter) and the many particles ($N\\to \\infty$) limits.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomasz Dębiec (University of Warsaw) DTSTART:20201125T135000Z DTEND:20201125T141000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/20 DESCRIPTION:Title: Incompressible limit for a two-species model with coupling through B rinkman’s law.\nby Tomasz Dębiec (University of Warsaw) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis \n\n\nAbstract\nWe study a two-species model of tissue growth describin g dynamics under mechanical pressure and cell growth. The pressure is inco rporated into the common fluid velocity through an elliptic equation\, cal led Brinkman’s law\, which accounts for viscosity effects in the individ ual species. \nOur aim is to establish the incompressible limit as the sti ffness of the pressure law tends to infinity - thus demonstrating a rigoro us bridge between the population dynamics of growing tissue at a density l evel and a geometric model thereof.\n
\n\nJoint work with B. Pertham
e (Sorbonne)\, M. Schmidtchen (TU Dresden) and N. Vauchelet (Paris 13). \n
LOCATION:https://researchseminars.org/talk/BIRS_20w5188/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mária Lukácová-Medvidová (Johannes Gutenberg-Universität Main
z)
DTSTART:20201125T150000Z
DTEND:20201125T152000Z
DTSTAMP:20260422T185749Z
UID:BIRS_20w5188/21
DESCRIPTION:Title: Viscoelastic phase separation: analysis and numerics\nby Mária
Lukácová-Medvidová (Johannes Gutenberg-Universität Mainz) as part of B
IRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis\
n\n\nAbstract\nMathematical modelling and numerical simulations of phase
separation becomes much\nmore involved if one component is a macromolecula
r compound. In this case\, the large molecular relaxation time\ngives rise
to a dynamic coupling between intra-molecular processes and the unmixing
on experimentally relevant time scales\,\nwith interesting new phenomena\,
for which the name “viscoelastic phase separation” has been coined.\
n
\nOur model of viscoelastic phase separation describes time evolutio
n of the volume fraction of a polymer and the bulk stress\nleading to a st
rongly coupled (possibly degenerate) cross-diffusion system. The evolution
of volume fraction is governed\nby the Cahn-Hilliard type equation\, w
hile the bulk stress is a parabolic relaxation equation. The system is fur
ther\ncombined with the Navier-Stokes-Peterlin system\, describing time e
volution of the velocity and (elastic) conformation tensor.\n
\nUnder
some physically relevant assumptions on boundedness of\nmodel parameters w
e have proved that global in time weak solutions exist.\nFurther\, we have
derived a suitable notion of the relative energy taking into account the
non-convex nature of the energy law\nfor the viscoelastic phase separation
. This allows us to prove the weak-strong uniqueness principle\nand conseq
uently the uniqueness of a weak solution in special cases.\n
\nOur exte
nsive numerical simulations confirm robustness of the analysed model\nand
the convergence of a suitable numerical scheme with respect to the relativ
e energy.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5188/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Degond (Imperial College London)
DTSTART:20201125T152500Z
DTEND:20201125T154500Z
DTSTAMP:20260422T185749Z
UID:BIRS_20w5188/22
DESCRIPTION:Title: Topological protection in collective dynamics\nby Pierre Degond
(Imperial College London) as part of BIRS workshop: Multiscale Models for
Complex Fluids: Modeling and Analysis\n\n\nAbstract\nStates of matter (suc
h as solid\, liquid\, etc) are characterized\nby different types of order
associated with local invariances under\ndifferent transformation groups.
Recently\, a new notion of topological\norder\, popularized by the 2016 ph
ysics nobel prize awarded to Haldane\,\nKosterlitz and Thouless\, has emer
ged. It refers to the global rigidity of\nthe system arising in some circu
mstances from topological constraints.\nTopologically ordered states are e
xtremely robust i.e. « topologically\nprotected » against localized pert
urbations. Collective dynamics occurs when\na system of self-propelled par
ticles organizes itself into a coherent\nmotion\, such as a flock\, a vort
ex\, etc. Recently\, the question of realizing\ntopologically protected co
llective states has been raised. In this work\, we\nconsider a system of s
elf-propelled solid bodies interacting through local\nfull body alignment
up to some noise. In the large-scale limit\, this system\ncan be described
by hydrodynamic equations with topologically non-trivial\nexplicit soluti
ons. At the particle level\, these solutions persist for a\ncertain time b
ut eventually decay towards a uniform flocking state\, due to\nthe stochas
tic nature of the particle system. We show numerically that the\npersisten
ce time of these topologically non-trivial solutions is far longer\nthan f
or topologically trivial ones\, showing a new kind of « topological\nprot
ection » of a collective state. To our knowledge\, it is the first time\n
that a hydrodynamic model guides the design of topologically non-trivial\n
states of a particle system and allows for their quantitative analysis and
\nunderstanding. In passing\, we will raise fascinating mathematical quest
ions\nunderpinning the analysis of collective dynamics systems. \n
\nJ
oint\nwork with Antoine Diez and Mingye Na (Imperial College London)\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5188/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbora Benesova (Charles University)
DTSTART:20201125T155000Z
DTEND:20201125T161000Z
DTSTAMP:20260422T185749Z
UID:BIRS_20w5188/23
DESCRIPTION:Title: A variational approach to fluid-structure interaction\nby Barbor
a Benesova (Charles University) as part of BIRS workshop: Multiscale Model
s for Complex Fluids: Modeling and Analysis\n\n\nAbstract\nIn this talk we
consider the interaction of a Stokes/Navier-Stokes flow with a viscoelast
ic body. The elastic body is allowed to undergo large deformations (but no
self-collisions). In order to handle this situation correctly\, we devise
a variational approximation scheme in the spirit of DeGiorgi to the combi
ned problem. Moreover\, by using a two-scale scheme\, we also extend this
approach to the hyperbolic regime including inertia of the solid body. The
se variational approaches allow us to prove proper energetic estimates whi
le also controling the geometric restictions posed on the solid body and\,
eventually\, to establish existence of weak solutions. This is joint work
with Malte Kampschulte and Sebastian Schwarzacher (both Prague).\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5188/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Gwiazda (Polish Academy of Sciences)
DTSTART:20201125T170000Z
DTEND:20201125T172000Z
DTSTAMP:20260422T185749Z
UID:BIRS_20w5188/24
DESCRIPTION:Title: Homogenization of nonlinear elliptic systems in nonreflexive Musiela
k-Orlicz spaces\nby Piotr Gwiazda (Polish Academy of Sciences) as part
of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Anal
ysis\n\n\nAbstract\n
We study the homogenization process for families of strongly nonlinear elliptic systems with the homogeneous Dirichlet bounda ry conditions. The growth and the coercivity of the elliptic operator is a ssumed to be indicated by a general inhomogeneous anisotropic N−function \, which may be possibly also dependent on the spatial variable\, i.e.\, t he homogenization process will change the characteristic function spaces a t each step.\n
\nSeveral notions of weak or 'very weak' solutions have been suggested for the incompressible and\ncompressible Euler systems\, motivated by the lack of a satisfactory well-posedness theory for these\nequations in turbulent regimes. Surprisingly\, the speaker and L. Székelyhidi showed in 2012 th at dis-\ntributional and measure-valued solutions are in a sense the same\ , although the latter had been expected\nto be a much weaker notion. In th is talk\, we turn to the isentropic compressible Euler system\, where\nthe situation is fundamentally different. \n
\nJoint work with E. Chiod aroli\, E. Feireisl\, O. Kreml\, and D.\nGallenmüller. \n
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Vaclav Macha (Academy of Sciences\, Czech Republic) DTSTART:20201125T175000Z DTEND:20201125T181000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/26 DESCRIPTION:Title: On a body with a cavity filled with compressible fluid\nby Vacla v Macha (Academy of Sciences\, Czech Republic) as part of BIRS workshop: M ultiscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\nWe concern the system consisting of a moving body filled with a compres sible fluid. We present several existence proofs\, however\, our main aim is to deal with the long-time behavior of the whole system. \n
\nRe sults presented during this work were done in collaboration with G. P. Gal di\, S. Nečasová and B. She.
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Yong Lyu (Nanjing University) DTSTART:20201126T130000Z DTEND:20201126T132000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/27 DESCRIPTION:Title: Homogenization of stationary Navier–Stokes–Fourier system in dom ains with tiny holes\nby Yong Lyu (Nanjing University) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n\n \nAbstract\nWe study the homogenization of stationary compressible Navier –Stokes–Fourier system in a bounded three dimensional domain perforate d with a large number of very tiny holes. Under suitable assumptions impos ed on the smallness and distribution of the holes\, we show that the homog enized limit system remains the same in the domain without holes.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Emmanuel Jabin (University of Maryland) DTSTART:20201126T132500Z DTEND:20201126T134500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/28 DESCRIPTION:Title: Compressible Navier-Stokes equations with heterogeneous pressure law s\nby Pierre-Emmanuel Jabin (University of Maryland) as part of BIRS w orkshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n\n\n Abstract\nWe prove the existence of global weak solutions à la Leray for compressible Navier-Stokes equations with a pressure law which depends on the density and on time and space variables t and x. The assumptions on th e pressure contain only locally Lipschitz assumption with respect to the d ensity variable and some hypothesis with respect to the extra time and spa ce variables. It may be seen as a first step to consider heat-conducting N avier-Stokes equations with physical laws such as the truncated virial ass umption. The paper focuses on the construction of approximate solutions th rough a new regularized and fixed point procedure and on the weak stabilit y process taking advantage of the new method introduced by the two first a uthors with a careful study of an appropriate regularized quantity linked to the pressure.In the talk\, we discuss a response of the fluid on the boundary\, which acts as a delayed slip due to material properties. In the moment when the slip changes rapidly\, the wall shear s tress and the slip can exhibit a sudden overshoot and subsequent relaxatio n. When these effects become significant\, the so-called dynamic slip phen omenon occurs. We develop a mathematical analysis of Navier-Stokes-like pr oblems with dynamic slip boundary condition\, which requires a proper gene ralisation of the Gelfand triplet and the corresponding function spaces se tting. \n
\n\nIt is a joint work with Anna Abbatiello and Miroslav B ulíček.\n
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie Doumic (INRIA) DTSTART:20201126T152500Z DTEND:20201126T154500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/31 DESCRIPTION:Title: Estimating the division of amyloid fibrils\nby Marie Doumic (INR IA) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeli ng and Analysis\n\n\nAbstract\n\nAmyloid fibrils are important biologic al structures associated with devastating human diseases such as Alzheimer disease\, as well as have vital biological functions such as adhesion and biofilm formation. The division of amyloid protein fibrils is required fo r the propagation of the amyloid state and is an important contributor to their stability\, pathogenicity\, and normal function. \nWe apply asymptot ic results on the fragmentation equation to develop an inverse problem ap proach\, allowing us to compare the division stability of amyloid fibrils and estimate their division features (fragmentation rate and kernel).\n
\n\nThis is a joint work with Magali Tournus\, Miguel Escobedo and We i-Feng Xue.
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Petr Kaplicky (Charles University) DTSTART:20201126T155000Z DTEND:20201126T161000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/32 DESCRIPTION:Title: Uniqueness and regularity of flows of non-Newtonian fluids with crit ical power-law growth\nby Petr Kaplicky (Charles University) as part o f BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analys is\n\n\nAbstract\nWe deal with the flows of non-Newtonian fluids in thr ee dimensional setting subjected to the homogeneous Dirichlet boundary con dition. Under the natural monotonicity\, coercivity and growth condition o n the Cauchy stress tensor expressed by a critical power index $p=\\frac{1 1}{5}$ we show that a Gehring type argument is applicable which allows to improve regularity of any weak solution. Improving further the regularity of weak solutions along a regularity ladder allows to show that actually s olution belongs to a uniqueness class provided data of the problem are suf ficiently smooth.\n
\n\nWe also briefly discuss if the similar techn ique is applicable to critical Convective Brinkman-Forchheimer equation.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Michal Bathory (University of Vienna) DTSTART:20201126T170000Z DTEND:20201126T172000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/33 DESCRIPTION:Title: Analysis of an unsteady flow of an incompressible heat-conductive ra te-type viscoelastic fluid with stress diffusion\nby Michal Bathory (U niversity of Vienna) as part of BIRS workshop: Multiscale Models for Compl ex Fluids: Modeling and Analysis\n\n\nAbstract\nViscoelastic fluids often exhibit high sensitivity of material properties on temperature changes. Ne vertheless\, the available mathematical theory for these fluids concerns o nly models that are isothermal or that are simplified in other ways. For e xample\, one can find existence theories in 2D\, for small data\, with onl y the corotational derivative\, with only the spherical part of the elasti city tensor etc. In the talk\, we introduce an existence theory without an y of these assumptions and treat a rather general class of Johnson-Segalma n-like models including full thermal evolution. To avoid the well-known il l-posedness of the corresponding PDE system\, we modify the ``elastic part '' of the dissipation of the fluid far from the equilibrium\, while preser ving thermodynamic compatibility of the model. This way\, we are able to p rove the existence of a global-in-time weak solution for any initial datum with finite total energy and entropy.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Paige Davis (Charles University) DTSTART:20201126T172500Z DTEND:20201126T174500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/34 DESCRIPTION:Title: Absolute Instabilities of Travelling Waves Solutions in a KellerSege l Model\nby Paige Davis (Charles University) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract \nThe Keller-Segel model for bacterial chemotaxis supports travelling wave solutions which have been described in the literature as both linearly st able and unstable and in the case of linear consumption (conditionally) no nlinearly stable. We reconcile this apparent contradiction by locating th e essential spectrum\, absolute spectrum and point spectrum of the linear operators associated with the travelling wave solutions. We derive conditi ons for the spectral (in)stability of the travelling wave solutions and th e critical parameters that indicate a transition from a transient to absol ute instability. Furthermore\, we show that the absolute spectrum deforms as the consumption is changed\, illustrating a connection between the cons tant\, sublinear and linear cases.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Fusco (Universita di Napoli) DTSTART:20201126T175000Z DTEND:20201126T181000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/35 DESCRIPTION:Title: Stability results for the nonlocal Mullins-Sekerka flow\nby Nico la Fusco (Universita di Napoli) as part of BIRS workshop: Multiscale Model s for Complex Fluids: Modeling and Analysis\n\n\nAbstract\nThe nonlocal Mu llins-Sekerka flow can be seen as the $H^{-\\frac12}$-gradient flow of the so called sharp-interface Ohta-Kawaski energy. In this talk we will show that three-dimensional periodic configurations that are strictly stable wi th respect to this energy are exponentially stable also for the nonlocal M ullins-Sekerka flow. This result is contained in a joint paper with E. Ace rbi\, M. Morini and V. Julin\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Dongjuan Niu (Capital Normal University) DTSTART:20201127T132500Z DTEND:20201127T134500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/36 DESCRIPTION:Title: Vanishing porosity limit of the coupled Stokes-Brinkman system\n by Dongjuan Niu (Capital Normal University) as part of BIRS workshop: Mult iscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\n
In this talk\, I will discuss with the small porosity asymptotic behavior of the coupled Stokes-Brinkman system in the presence of a curved interfac e between the Stokes region and the Brinkman region. In particular\, we de rive a set of approximate solutions\, validated via rigorous analysis\, to the coupled Stokes-Brinkman system. Of particular interest is that the ap proximate solution satisfies a generalized Beavers-Joseph-Saffman-Jones in terface condition (1.9) with the constant of proportionality independent o f the curvature of the interface. \n
\nIt is a joint work with Mingw en Fei and Xiaoming Wang.
\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Sébastien Boyaval (Ecole des Ponts ParisTech & Inria Paris) DTSTART:20201127T135000Z DTEND:20201127T141000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/37 DESCRIPTION:Title: Viscoelastic motions of Maxwell fluids with finite propagation speed \nby Sébastien Boyaval (Ecole des Ponts ParisTech & Inria Paris) as p art of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and A nalysis\n\n\nAbstract\nIn continuum models for non-perfect fluids\, viscoe lastic stresses have often been introduced as extra-stresses of purely-dis sipative (entropic) nature\, \nsimilarly to viscous stresses that induce m otions of infinite propagation speed.\nA priori\, it requires only one to couple an evolution equation for the (extra-)stress with the momentum bala nce.\nIn many cases\, the apparently-closed resulting system is often not clearly well-posed\, even locally in time.\nThe procedure also raises ques tions about how to encompass transition toward alastic solids.\n\nA notice able exception is K-BZK theory where one starts with a purely elastic flui ds.\nViscoelasticity then results from dissipative (entropic) stresses due to the relaxation of the fluids'"memory".\nThat K-BKZ approach is physica lly appealing\, but mathematically quite difficult because integrals are i ntroduced to avoid material ('natural') configurations.\n\nWe propose to i ntroduce viscoelastic stress starting with hyperelastic fluids (like K-BKZ ) and evolving material configurations (unlike K-BKZ).\nAt the price of an enlarged system with an additional material-metric variable\,\none can de fine well-posed (compressible) motions with finite propagation speed\nthro ugh a system of conservation laws endowed with a "contingent entropy" (lik e in standard polyconvex elastodynamics).\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Milan Pokorný (Charles University) DTSTART:20201127T150000Z DTEND:20201127T152000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/38 DESCRIPTION:Title: Existence analysis of a stationary compressible fluid model for heat -conducting and chemically reacting mixtures\nby Milan Pokorný (Charl es University) as part of BIRS workshop: Multiscale Models for Complex Flu ids: Modeling and Analysis\n\n\nAbstract\nWe present large-data existence result for weak solutions to a steady compressible\nNavier-Stokes-Fourier system for chemically reacting fluid mixtures.\nGeneral free energies sati sfying some structural assumptions are considered\,\nwith a pressure conta ining a $\\gamma$-power law.\nThe model is thermodynamically consistent an d contains the Maxwell-Stefan\ncross-diffusion equations in the Fick-Onsag er form\nas a special case. Compared to previous works\, a very general mo del class is\nanalyzed\, including cross-diffusion effects\, temperature g radients\,\ncompressible fluids\, and different molar masses.\nA priori es timates are derived from the entropy balance and the total\nenergy balance . The compactness for the total mass density follows from\nan estimate for the density in $L^{\\gamma}$ with $\\gamma>3/2$\,\nthe effective viscous \nflux identity\, and uniform bounds related to Feireisl's oscillations de fect measure.\nThese bounds rely heavily on the convexity of the free ener gy and the strong convergence\nof the relative chemical potentials.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomas Los (Charles University) DTSTART:20201127T152500Z DTEND:20201127T154500Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/39 DESCRIPTION:Title: On planar flows of viscoelastic fluids of the Burgers type\nby T omas Los (Charles University) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\nRate-type fluid m odels involving the stress and its observer-invariant time derivatives of higher order are used to describe a large class of viscoelastic mixtures - geomaterials like asphalt\, biomaterials such as vitreous in the eye\, sy nthetic rubbers such as SBR. A standard model that belongs to the category of viscoelastic rate-type fluid models of the second order is the model d ue to Burgers\, which can be viewed as a mixture of two Oldroyd-B models o f the first order. This viewpoint allows one to develop the whole hierarch y of generalized models of a Burgers type. We study one such generalizatio n. Carrying on the study by \nMasmoudi (2011)\, who briefly proved the wea k sequential stability of weak solutions to the Giesekus model\, we prove long time and large data existence of weak solutions to a mixture of two G iesekus models in two spatial dimensions.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Jakub Skrzeczkowski (University of Warsaw) DTSTART:20201127T155000Z DTEND:20201127T161000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/40 DESCRIPTION:Title: Fast reaction limit with nonmonotone reaction function\nby Jakub Skrzeczkowski (University of Warsaw) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\n\nWe a nalyse fast reaction limit in the reaction-diffusion system\n\\begin{align *}\n\\partial_t u^{\\varepsilon} &= \\frac{v^{\\varepsilon} - F(u^{\\vare psilon})}{\\varepsilon}\, \\\\\n\\partial_t v^{\\varepsilon} &= \\Delta v^ {\\varepsilon} + \\frac{F(u^{\\varepsilon}) - v^{\\varepsilon}}{\\varepsil on}\,\n\\end{align*}\nwith nonmonotone reaction function $F$. As speed of reaction tends to infinity\, the concentration of non-diffusing component $u^{\\varepsilon}$ exhibits fast oscillations. We identify precisely its Y oung measure which\, as a by-product\, proves strong convergence of the di ffusing component $v^{\\varepsilon}$\, a result that is not obvious from a priori estimates. Our work is based on analysis of regularization for for ward-backward parabolic equations by Plotnikov [2]. We rewrite his ideas i n terms of kinetic functions which clarifies the method\, brings new insig hts\, relaxes assumptions on model functions and provides a weak formulati on for the evolution of the Young measure.\n
\n\n\nThis is a joint w ork with Beno\\^\\i t Perthame (Paris) [1]\n
\n\n\n[1] B. Perthame\,
J. Skrzeczkowski. Fast reaction limit with nonmonotone reaction functi
on.\narXiv: 2008.11086\, submitted.
\n[2] P. I. Plotnikov. Passa
ge to the limit with respect to viscosity in an equation with a variable d
irection of parabolicity. Differ. Uravn.\, 30:4 (1994)\, 665--674\; Di
ffer. Equ.\, 30:4 (1994)\, 614--622.\n
We consider the Kelvin-Voigt model for viscoelasticity and prove propagation of $H^1$-regularity for the deformation gradient of wea k solutions in two and three dimensions assuming that the stored energy sa tisfies the Andrews-Ball condition\, in particular allowing for a non-mono tone stress. By contrast\, a counterexample indicates that for non-monoton e stress-strain relations (even in 1-d) initial oscillations\nof the strai n lead to solutions with sustained oscllations. In addition\, in two space dimensions\, we prove that the weak solutions with deformation gradient i n $H^1$ are in fact unique\, providing a striking analogy to the 2D Euler equations with bounded vorticity. \n
\n\n(joint work with K. Koumato s (U. of Sussex)\, C. Lattanzio and S. Spirito (U. of L’Aquila)).\n
\ n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Agnieszka Świerczewska-Gwiazda (University of Warsaw) DTSTART:20201127T175000Z DTEND:20201127T181000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/43 DESCRIPTION:Title: Dissipative measure-valued solutions for the Euler-Poisson equation< /a>\nby Agnieszka Świerczewska-Gwiazda (University of Warsaw) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis \n\n\nAbstract\nWe consider pressureless compressible Euler equations dri ven by nonlocal repulusion-attraction and alignment forces. Our attention is directed to measure-valued solutions\, i.e.\, very weak solutions desc ribed by a\nclassical Young measure together with appropriate concentratio n defects. We investigate the evolution of a relative energy functional t o compare\na measure-valued solution to a regular solution emanating from the same initial datum. This leads to a weak-strong uniqueness principle.\ n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Patel (University of Oxford) DTSTART:20201127T130000Z DTEND:20201127T132000Z DTSTAMP:20260422T185749Z UID:BIRS_20w5188/44 DESCRIPTION:Title: Existence of large-data global weak solutions to a model of a strai n-limiting viscoelastic body\nby Victoria Patel (University of Oxford) as part of BIRS workshop: Multiscale Models for Complex Fluids: Modeling and Analysis\n\n\nAbstract\nWe will consider a system of evolutionary PDEs that describe a model of\nviscoelastic bodies exhibiting a certain strain -limiting property. \nNamely\, working in the small strain setting\, we as k that a sum of the linearised \nstrain and the strain rate is given by so me function $F$ acting on the Cauchy\nstress tensor\, where this function $F$ is nonlinear and bounded. These \nmodels come from the much larger cla ss of implicit constitutive\nrelations. We will show the existence and uni queness of global-in-time\nlarge-data weak solutions to this strain-limiti ng problem by first\nproving the existence of solutions to a broader class of models. This \nbroader class replaces the bounded function $F$ on the stress by one that\nexperiences some level of polynomial growth. Using a s uitable approximation of the\nstrain-limiting problem by these problems wi th growth\, we are able to deduce\nsuitable a priori bounds that allow us to prove the existence of a \nsolution to our original problem. The main i ssue is that the stress tensor\, and\nthus approximations of the stress\, are initially seen to be bounded a priori \nonly in $L^1$. However\, we ar e able to circumvent such an issue without introducing \nany notion of mea sure-valued solutions\, and in particular\, we obtain a satisfactory \nexi stence theory for these problems under some suitable assumptions on the da ta.\n LOCATION:https://researchseminars.org/talk/BIRS_20w5188/44/ END:VEVENT END:VCALENDAR