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Liste des exposés

I. Nouvelles tendances en mécanique des fluides

II. Problèmes à frontière libre

III. Modèles mathèmatiques et méthodes numériques en mécanique des milieux continus

IV. Processus stochastiques

V. Maths et planète Terre

VI. Analyse et contrôle des EDP

VII. Statistiques

VIII. Analyse non-lisse et optimisation

Nouvelles tendances en mécanique des fluides

(cette liste est en processus d'actualisation)

List des exposés

1.
BOSTAN Mihai
Aix-Marseille Université - Centre de Mathématiques et Informatique, France
Titre: Multi-scale analysis for the Vlasov-Poisson equations (details)
Résumé:
We perform the mathematical analysis for the Vlasov-Poisson equations, in the magnetic confinement setting (large magnetic field). We justify the convergence toward the limit model, and investigate its main properties. The arguments rely on two-scale analysis combined to ergodic theory (average operators along unitary groups).
2.
BURTEA Cosmin
Université Paris-Est Créteil, France
Titre: New long time existence results for a class of Boussinesq-type systems (details)
Résumé:
In this talk we deal with the long time existence for the Cauchy problem associated to some asymptotic models for long wave, small amplitude gravity surface water waves. We generalize some of the results that can be found in the literature devoted to the study of Boussinesq systems by implementing an energy method on spectrally localized equations. In particular, we obtain better results in terms of the regularity level required to solve the initial value problem on large time scales and we do not make use of the positive depth assumption.
3.
CIUPERCA Sorin Ionel
Institut Camille Jordan - Université Claude Bernard Lyon 1, France
Titre: Existence et unicité d'une solution densité de probabilités pour une équation de Doi-Edwards stationnaire (details)
Résumé:
{\bf R\'esum\'e:} \ Le mod\ele de Doi-Edwards est bas\'e sur la th\'eorie cin\'etique et d\'ecrit la distribution des mol\'ecules dans un polym\ere fondu. Chaque mol\'ecule est repr\'esent\'e pour une courbe dans l'espace, appell\'ee chaine primitive et nous consid\'erons une distribution de ces mol\'ecules selon deux variables dites microscopique: $$s \in [0, 1]$$ et $$u \in S_2$$ qui repr\'esentent respectivement une coordonn\'ee courviligne normalis\'ee et l'orientation dans l'espace (ici $$S_2$$ est la sph\ere unite dans $$\R^3$$). Dans sa variante stationnaire, l'\'equation de Doi-Edwards s'\'ecrit: trouver $$F = F(s,u)$$ (qui est la densit\'e de distribution des mol\'ecules) telle que % $$\label{eq1} \begin{cases} - \frac{\partial^2 F}{\partial s^2} + \frac {\partial} {\partial u} (\mathcal{G} F) - \alpha F k u \cdot u + \alpha \frac {\partial} {\partial s} [F k : \lambda(F)] = 0 \\ F(s=0) = F(s=1) = \frac 1 {4 \pi}. \end{cases}$$ % Dans cette \'equation $$\alpha \geq 0$$ est un param\etre physique, $$k \in \mathcal{M}_3(\R)$$ est le gradient de vitesse du fluide, suppos\'e connu, $$\mathcal{G} = ku - ku \cdot u u$$ et $\lambda(F)(s) = \int_0^s \int_{S_2} F(s', u) \, u \otimes u \, du \, ds'.$ Nous montrons, pour $$\alpha$$ proche'' de 0, l'existence et l'unicit\'e d'une solution de \eqref{eq1} et le fait que cette solution est une densit\'e de probabilit\'e en $$u$$.
4.
FANELLI Francesco
Institut Camille Jordan - Université Claude Bernard Lyon 1, France
Titre: On some models of non-homogeneous inviscid fluids (details)
Résumé:
In this talk we review recent results on strong solutions theory for some models of inviscid fluids with variable density. In the first part we will be concerned with the well-posedness of Euler equations in critical spaces, and with the propagation of geometric structures related to the vortex patch configuration. In the second part, we will turn the attention to a zero-Mach number system, derived by Alazard from the incompressible limit of the full compressible Euler equations. After making a connection with other quasi-incompressible models, and with the problem of propagation of interfaces, we will study its well-posedness in critical spaces.
5.
IFTIMIE Dragos
Université Lyon 1, France
Titre: Self-similar point vortices and confinement of vorticity (details)
Résumé:
We discuss several issues on the large time behavior of solutions of the incompressible Euler equations in dimension two. The point-vortex system, a discrete version of the Euler equations, gives a good indication on what this large time behavior should be. Of particular interest are the so-called self-similar configurations of point vortices which either collapse to a point or, when reversing time, grow to infinity like the square root of the time. We consider such a self-similar configuration of point vortices and we find a condition on the point vortices such that a vorticity initially confined around one point vortex will remain confined around the point vortex. We will also discuss its relevance to the large time behavior of the Euler equations. This is joint work with Carlo Marchioro.
6.
KOLUMBAN Jozsef
Université Paris Dauphine, France
Titre: Control of the motion of a rigid body immersed in a perfect two-dimensional fluid (details)
Résumé:
We consider the motion of a rigid body immersed in a two-dimensional irrotational perfect fluid. The fluid is assumed to be confined in a bounded domain. We achieve exact controllability of the solid by using impulsive boundary control on the fluid. We treat separately the case when there is no circulation around the solid, then we extend our controllability result to the case with circulation using topological and time-rescale arguments.
7.
LEFTER Catalin
Univ.Al.I.Cuza, Romania
Titre: Boundary stabilization of fluid dynamics. An operatorial approach (details)
Résumé:
We intend to present an operatorial approach to the problem of boundary stabilization and control of Navier-Stokes type equations. We analyze the observability inequalities corresponding to various situations for the boundary control, entering the equation through non-slip (Dirichlet) or slip type (Navier) boundary conditions/
8.
MIOT Evelyne
CNRS - Université Grenoble Alpes, France
Titre: On the convergence of the Vlasov-Poisson system to the Euler equation in the gyrokinetic limit (details)
Résumé:
We investigate the gyrokinetic limit for the Vlasov-Poisson equation in two dimensions. In an appropriate asymptotic regime, we extend a result by L. Saint-Raymond on the convergence of the solutions towards a weak vorticity solution of the 2D Euler equation.
9.
MONNIAUX Sylvie
Université Aix-Marseille, France
Titre: The Dirichlet-to-Neumann problem associated with the Stokes operator (details)
Résumé:
On a bounded strongly Lipschitz domain, we define the Stokes operators associated with homogeneous Dirichlet and Neumann boundary conditions in the space $$L^2$$. Using the Dirichlet-to-Neumann operator associated with the Stokes operator, we prove that their eigenvalues compare the same way the eigenvalues of the Laplacian with homogeneous Dirichlet and Neumann boundary conditions compare, as in Friedlander's result.
10.
PIERRE Olivier
LMJL, University of Nantes, France
Titre: Analytic current-vortex sheets in incompressible magnetohydrodynamics (details)
Résumé:
Current-vortex sheets are a particular tangential discontinuity in magnetohydrodynamics (MHD). This is a well-known problem since the 1950's: it models the coupling between two plasmas separated by a free surface $$\Gamma(t)$$ ($$t$$ is the time variable), which give rise to a tangential discontinuity across $$\Gamma(t)$$. More precisely, vortices'' are created around the free surface $$\Gamma(t)$$ because of the jumps of the tangential velocity and the tangential magnetic field. The free surface is thus called \textit{current-vortex sheet}. We will show how to construct \textit{analytic solutions} to the current-vortex sheet problem, using a Cauchy-Kowalevskaya theorem. To do so, we begin with reducing the problem into a \textit{fixed} domain in a suitable way, as is common for free boundary problems. Afterwards, we introduce some Banach spaces of analytic functions, satisfying crucial differentiation and algebra properties. Such Banach spaces will allow us to compute analytic estimates associated with the \textit{front} of the discontinuity and the so-called \textit{total pressure} in order to conclude with a Cauchy-Kowalevskaya theorem.
11.
SCROBOGNA Stefano
University of Bordeaux, France
Titre: On fastly rotating and weakly compressible fluids (details)
Résumé:
his exposition is focused on the dynamics of inviscible, fasly rotating and slightly barotropic hydrodynamical flows. In the regime in which Rossby numer and Mach numbers tend to zero at the same rate there are present two-types of dispersive effect, due respectively to high-speed propagation of acoustic waves and centrifugal effects, these effects can be studied combined via Strickartz estimates. We prove that these pertubations, altough they propagate at a speed , converge strongly to zero in some appropriate space. This allows us to prove that the limit hydrodynamic flow is globally well posed in for although it is a 3D flow. Joint work with Ngo Van-Sang.
12.
TRESCASES Ariane
Univ. Cambridge, UK
Titre: Régularité de l'équation de Boltzmann en domaine borné (details)
Résumé:
L’équation de Boltzmann modélise l’évolution de la densité de particules d’un gaz raréfié. En domaine borné (avec réflexion diffusive au bord), la solution présente un comportement singulier sur les trajectoires rasant le bord du domaine. Dans le cas d’un domaine convexe, les singularités sont confinées au bord rasant, alors que dans le cas d’un domaine non-convexe, certaines trajectoires singulières pénètrent le domaine et des discontinuités peuvent se propager à l’intérieur. Nous étudions la question de la régularité de la solution dans les deux cas.

Participants

1.
BALASOIU Dimitri
Laboratoire Jean Kuntzmann, France
2.
BENYO Krisztian
Université de Bordeaux, France
3.
Institut Camille Jordan -Universite Jean Monnet, France
4.
CANDEA Doina
Universitatea Politehnica Bucuresti, Romania
5.
CARJA Ovidiu
Al.I. Cuza University, Romania
6.
CEUCA Razvan-dumitru
Universitatea Alexandru Ioan Cuza Iasi, Romania
7.
COJOCEA Manuela - Simona
Faculty of Mathematics and Computer Science, University of Bucharest, Romania
8.
9.
DELIA Coculescu
University of Zurich, Switzerland
10.
GABRIELA Tanase
UAIC, Facultatea de Matematica, Romania
11.
IACOB Ioana
"Alexandru Ioan Cuza" University, Iasi, Romania, Romania
12.
ICHIM Andrei
Université "Blaise Pascal" Clermont-Ferrand, France
13.
IGNAT Liviu
Institutul de Matematica Simion Stoilow, Romania
14.
IGNAT Tatiana Ionica
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania
15.
JOURANI Abderrahim
Université de Bourgogne Franche-Comté, France
16.
PREDA Cristian
Université de Lille et ISMMA Gh. Mihoc - C. Iacob, France/Roumanie
17.