6. 1. 2009
9:00pracovní seminář NCMM
Na pracovním semináři vystoupí Miroslav Bulíček a Tomáš Bárta.
13. 1. 2009
9:00Josef Štěpán (
MFF UK Praha):
Stochastické reprezentace parciálních diferenciálních rovnic
Abstrakt: pdf
Přednáška bude v češtině.
20. 1. 2009
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.
24. 2. 2009
9:00Reinhard Farwig (Technical University Darmstadt): Global Weak Solutions of the Instationary Navier-Stokes System with Non-zero Boundary Values
10. 3. 2009
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
17. 3. 2009
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
24. 3. 2009
Giuseppe 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.
Jörg 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
31. 3. 2009
László 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.
Antonín Novotný (University of Toulon): Singular limits in the thermodynamics of viscous fluids - part III
7. 4. 2009
Andrea Cianchi (University of Firenze): TBA
Vuk 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.
Nikolai 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.
9. 4. 2009
Workshop on the occassion of 60th anniversary of prof. Jiří Neustupa
Speakers: 9:00-9:20 Antonín Novotný, 9:25-10:10 Miloslav Feistauer, 10:10-10:30 break, 10:30-11:15 Reimund Rautmann, 11:25-12:10 Reiner Picard, 12:20-13:00 Patrick Penel
Organized by Institute of Mathematics of the AS CR and Faculty of Civil Engineering, Czech Technical University in Prague.
14. 4. 2009
Maurizio Grasselli (
Politecnico di Milano):
Asymptotic behavior of dissipative evolution equations - Part II
Dissipative dynamical systems: bounded absorbing sets, attracting sets, compactness and asymptotic compactness, global attractors and their properties, existence theorems, dynamics on the attractor, Lyapunov functionals and gradient systems, unstable and stable manifolds, characterization of global attractors for gradient systems. (Part I takes place on 6th April at the Necas seminar on continuum mechanics)
Andrea Cianchi (University of Firenze): TBA
21. 4. 2009
Maurizio Grasselli (Politecnico di Milano): Asymptotic behavior of dissipative evolution equations - Part III
Reaction-diffusion equations: well-posedness, bounded absorbing sets, compact absorbing sets, global attractor, further related examples (3D NS equation, Cahn-Hilliard equation, phase-field systems, two-phase fluids).
Enrich 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.
Andrea Cianchi (University of Firenze): TBA
28. 4. 2009
Maurizio Grasselli (Politecnico di Milano): Asymptotic behavior of dissipative evolution equations - Part IV
Damped semilinear wave equations: well-posedness, critical growth, the 3D case (bounded abosrbings sets, compact attracting sets, global attractor).
Andrea Cianchi (University of Firenze): TBA
Roger Lewandowski (University Rennes 1): TBA
5. 5. 2009
Victor Isakov (Department of Mathematics and Statistics, Wichita State University): TBA
Roger Lewandowski (University Rennes 1): TBA
Roger Lewandowski (University Rennes 1): TBA
19. 5. 2009
Roman Shvydkoy (University of Illinois, Chicago): TBA
Případná změna programu semináře bude oznámena Emilem.
