9:00pracovní seminář NCMM
Na pracovním semináři vystoupí Miroslav Bulíček a Tomáš Bárta.
9:00Josef Štěpán (
MFF UK Praha):
Stochastické reprezentace parciálních diferenciálních rovnic
Abstrakt: pdf
Přednáška bude v češtině.
9:00Mohamed Majdoub (
University Tunis ElManar):
Energy Critical NLS in two space dimensions
We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity
We identify subcritical, critical and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case. We also obtain a scattering result in the subcritical regime.
10:15Yutaka Terasawa (Nečas Center and Sapporo University): On Stokes operators with variable viscosity
We consider a genaralization of the Stokes resolvent equation, where the constant viscosity is replaced by a general given positive function bounded from below by a positive constant. This system arises as a linearized system in several fluid mechanics problems. We prove that an associated Stokes-like operator generates an analytic semi-group and admits a bounded $ H_{\infty} $ calculus in $ L^q $ space, which implies the maximal $ L^q $ regularity of the corresponding parabolic evolution equation. The analysis is done for both bounded domains and some class of unbounded domains with boundary of low regularity.
9:00Reinhard Farwig (Technical University Darmstadt): Global Weak Solutions of the Instationary Navier-Stokes System with Non-zero Boundary Values
9:00Bernard Ducomet (Universite Bruyeres, France): Asymptotics for a fluid model of neutron star, after Lattimer
10:15Okihiro Sawada (Waseda University, Tokyo): On the incompressible Navier-Stokes flows around various steady states in the whole space
9:00Jörg Wolf (
University of Magdeburg):
Existence of suitable weak solutions to the Navier-Stokes-Fourier system and partial regularity - Part I
Second lecture of the short course "On the existence and regularity of weak solutions to the Navier-Stokes-Fourier systems under Dirichlet boundary conditions".
Full abstract: pdf
10:15Jörg Wolf (
University of Magdeburg):
Existence of suitable weak solutions to the Navier-Stokes-Fourier system and partial regularity - Part II
Third lecture of the short course "On the existence and regularity of weak solutions to the Navier-Stokes-Fourier systems under Dirichlet boundary conditions".
Full abstract: pdf
9:00Giuseppe Mingione (University of Parma): Non linear aspects of Calderon-Zygmund theory
Calderon-Zygmund theory is a classical tool allowing, in the linear case, to sharply infer the integrability information on solutions to elliptic and parabolic equations starting from that of the given data. I will try to report on some non-linear analogues of such results.
10:15Jörg Wolf (
University of Magdeburg):
Existence of renormalized solutions to the Navier-Stokes-Fourier system and partial regularity
Last lecture of the short course "On the existence and regularity of weak solutions to the Navier-Stokes-Fourier systems under Dirichlet boundary conditions".
Full abstract: pdf
9:00László Székelyhidi (University of Bonn): Convex Integration for Isometric Immersions and the Euler Equations
Since work of Nash and Kuiper in the 1950s the following dichotomy concerning isometric embeddings of $S^2$ into $\R^3$ is well known: whereas the only $C^2$ isometric embedding is the standard embedding modulo rigid motion, there exist many $C^1$ isometric embeddings which can "wrinkle up" the sphere inside arbitrarily small regions in space. It turns out that the same method can be used to construct many examples of weak solutions of the incompressible Euler equations which dissipate energy and are highly oscillatory. In the talk I will show the proof of this result, which is joint work with Camillo De Lellis. I will then address the question of what should be the borderline regularity between rigidity and flexibility for isometric immersions, and the analogous borderline between dissipative and energy-conserving solutions of the Euler equations. These questions are highly relevant in their own right, and seem very much related.
10:15Antonín Novotný (University of Toulon): Singular limits in the thermodynamics of viscous fluids - part III/IV
9:00Andrea Cianchi (University of Firenze): Orlicz-Sobolev spaces and applications to strongly nonlinear PDEs - part I/IV
Basic definitions and properties of Orlicz and Orlicz-Sobolev spaces.
Isoperimetric inequalities.
Symmetrization principles for Orlicz norms of the gradient.
Anisotropic symmetrization and anisotropic Orlicz-Sobolev spaces.
10:15Vuk Milisic (Wolfgang Pauli Institute, Vienna): Multi-scale blood flow modelling for stented arteries: theoretical and numerical results
Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Then, we investigate convergence of boundary layer approximations and the corresponding wall laws in the case of some realistic boundary conditions at the inlet and outlet parts of the domain. We derive error estimates in terms of the roughness size epsilon either in the a priori norm or in the very veak context (cf Necas). We show some numerical test validating our theoretical results.
11:30Nikolai V. Chemetov (CMAF / University of Lisbon): Strongly Nonlinear Hyperbolic - Elliptic Problem in a Bounded Domain
We investigate a mixed hyperbolic-elliptic type system of PDEs in a given domain. Motivated by physics, we consider nonzero boundary conditions, which describe a flow through the domain. We prove the solvability of this system, using a kinetic formulation of the problem. The system can be used for different physical situations, such as:
a) the motion of superconducting vortices in the superconductor;
b) the Keller-Segel model, describing the collective cell movement;
c) the porous media motion and etc.
Workshop Mathematical aspects of fluid mechanics and thermodynamics
In the occassion of 60th birthday of Prof. Jiří Neustupa.
Place: Blue lecture hall, Institute of Mathematics (ground floor of the building beyond the backyard), Žitná 25, Praha 1
Organized by Petr Kučera (Faculty of Civil Engineering, Czech Technical University in Prague) and Šárka Nečasová (Institute of Mathematics, Czech Academy of Sciences).
9:00-9:15Antonín Novotný (University of Toulon): opening
9:20-10:05Patrick Penel (
University of Toulon):
In occasion of sixtieth birthday of Jiří Neustupa: The main originality of three common studies in the theory of Navier-Stokes equations
The mathematical understanding of many qualitative aspects of classical 3D-Navier-Stokes flows is always a fascinating subject of research. Among central issues are the following questions : Nature of eventual singularities developed by the flows ? Influence of boundary conditions complemented the models ? Some related problems have been solved in these directions. The present lecture proposes a brief survey of three common small contributions obtained with Jiri Neustupa based on relatively new approaches. - New in 1996-97, we focused our attention on regularity information in dependance of specific smoothness of one velocity component (expecting the role of the vorticity and this fact that in case of blow'up all velocity components simultaneously loose their regularity).
- New in 2002-03, we weakened the three constraints of Dirichlet boundary conditions and preserved the usual results of the theory generalizing the impermeability properties (thinking that generally speaking the tangential part of the velocity has no reason to be zero on the boundary)
- New in 2008-09, we claimed and proved that the contacts or possible collisions of bodies moving in a fluid can occur with a natural non zero velocity if one consider Navier's boundary condition (a result we cannot expect with the Dirichlet boundary conditions).
10:05-10:50Miloslav Feistauer (Charles University in Prague): Numerical solution of compressible flow in time dependent domains
We are concerned with the simulation of inviscid and viscous compressible flow in time dependent domains. We present an ALE (Arbitrary Lagrangian-Eulerian) formulation of the Euler and Navier-Stokes equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. We present some computational results for flow in a channel with a moving wall.
These results were obtained in cooperation with Václav Kučera and Jaroslava Prokopová from Charles University in Prague, Faculty of Mathematics and Physics, and Jaromír Horáček from Institute of Thermomechanics of Academy of Sciences of the Czech Republic.
10:50-11:20break
11:20-12:05Reimund Rautmann (University of Paderborn): On very smooth Navier-Stokes solutions
Recent results on vorticity transport&diffusion [1] suggest the question, wether there are Navier-Stokes solutions taking their values in the domain of the Stokes operator´s power 3/2. We will find such solutions to Navier-Stokes initial-boundary value problems with outer forces which depend on the flow velocity in a special way proposed by V.A. Solonnikov.
[1] R.Rautmann: A direct approach to vorticity transport&diffusion, RIMS Koyuroku Bessatsu B1, Kyoto (2007)305-329.
12:05-12:50Reiner Picard (University of Dresden): On a model in poro-elasticity
A modification of the material law associated with the well-known Biot system as suggested by M. A. Murad and J. H. Cushman in 1996 and first rigorously investigated by R. E. Showalter in 2000 is re-considered in the light of a new approach to a comprehensive class of evolutionary problems and extended to large class of anisotropic inhomogeneous media.
The paper is joint work with Des McGhee (Glasgow, U.K.).
9:00Maurizio Grasselli (Politecnico di Milano): Asymptotic behavior of dissipative evolution equations - Part II/IV
Existence theorems for global attractors, dynamics on the global attractor, Lyapunov functionals and gradient systems, unstable and stable manifolds, global attractors for gradient systems.
10:15Andrea Cianchi (University of Firenze): Orlicz-Sobolev spaces and applications to strongly nonlinear PDEs - part II/IV
Embedding theorems for first-order Orlicz-Sobolev spaces.
Anisotropic Sobolev inequalities.
Embedding theorems for higher-order Orlicz-Sobolev spaces.
9:00Maurizio Grasselli (Politecnico di Milano): Asymptotic behavior of dissipative evolution equations - Part III/IV
Reaction-diffusion equations: well-posedness, bounded absorbing sets, compact absorbing sets, global attractor, further related examples (2D Navier-Stokes equation, Cahn-Hilliard equation, phase-field systems, two-phase fluids).
10:15Enrich Fernandez-Cara (University of Sevilla, Spain): Some recent results and open questions concerning the control of nonlinear PDEs from fluid mechanics
This talk concerns the formulation of control problems for some partial differential systems with origin in fluid mechanics: the Navier-Stokes and Boussinesq equations, quasi-geostrophic models, the Maxwell and Oldroyd viscoelastic models, etc. The most interesting results are connected to the local exact controllability to the trajectories. The particular properties of some of these systems lead to challenging open problems.
11:30Andrea Cianchi (University of Firenze): Orlicz-Sobolev spaces and applications to strongly nonlinear PDEs - part III/IV
Continuity and differentiability properties of Orlicz-Sobolev functions. Boundedness of solutions to variational problems under general growth conditions.
9:00Maurizio Grasselli (Politecnico di Milano): Asymptotic behavior of dissipative evolution equations - Part IV/IV
Damped semilinear wave equations: the 3D case with critical growth, the global attractor and its smoothness.
10:15Andrea Cianchi (University of Firenze): Orlicz-Sobolev spaces and applications to strongly nonlinear PDEs - part IV/IV
Local boundedness of solutions to fully anisotropic elliptic equations in divergence form. Higher-integrability properties of the gradient of solutions to variational problems under general growth conditions.
11:30Roger Lewandowski (University Rennes 1): TBA
9:00Roger Lewandowski (University Rennes 1): TBA
10:15Roger Lewandowski (University Rennes 1): TBA
9:00Victor Isakov (Department of Mathematics and Statistics, Wichita State University): TBA
Roman Shvydkoy (University of Illinois, Chicago): TBA
Případná změna programu semináře bude oznámena Emilem.
