Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview.
Explicit solutions of generalized nonlinear Boussinesq equations.
Explicit upper and lower bounds on the number of degrees of freedom for damped and driven cubic Schrödinger equations
Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique
Explosion pour l’équation de Schrödinger au régime du “log log”
On présente dans cet exposé des résultats récents de Merle et Raphael sur l’analyse des solutions explosives de l’équation de Schrödinger critique. On s’intéresse en particulier à leur preuve du fait que les solutions d’énergie négative (dont on savait qu’elles explosaient par l’argument du viriel) et dont la norme est proche de celle de l’état fondamental, explosent au régime du “log log”et que ce comportement est stable.
Exponential attractors for a nonclassical diffusion equation.
Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems
We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space for finite , partially answering...
Exponential decay to partially thermoelastic materials
We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.
Exponential of a hamiltonian in large subsets of a lattice and applications
Exponential stability and global attractors for a thermoelastic bresse system.
Exponential stability of two coupled second-order evolution equations.
Exponential Sums and Nonlinear Schrödinger Equations.
Exponentially slow traveling waves on a finite interval for Burger's type equation.
Extended soliton solutions in an effective action for Yang-Mills theory.
Extension of a regularity result concerning the dam problem
One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.
Exterior problem of the Darwin model and its numerical computation
In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell’s equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.
Exterior problem of the Darwin model and its numerical computation
In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell's equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.
-manifolds and integrable systems of hydrodynamic type
We investigate the role of Hertling-Manin condition on the structure constants of an associative commutative algebra in the theory of integrable systems of hydrodynamic type. In such a framework we introduce the notion of -manifold with compatible connection generalizing a structure introduced by Manin.
Familles de branches de bifurcations dans les équations de Ginzburg-Landau
Familles de convexes invariantes et équations de diffusion-réaction
Pour localiser la solution d’un système de diffusion-réaction, il suffit de construire une famille de convexes , invariante par rapport au champ de vecteurs associé à ce système; la solution est alors incluse dans à l’instant dès qu’elle est contenue dans à l’instant zéro. Les fonctions d’appui associées à de telles familles de convexes sont solutions d’un système différentiel, mais celui-ci peut également engendrer des familles non invariantes.