Propagation estimates for N-body Stark hamiltonians
Propagation et réflexion des singularités pour l'équation de Schrödinger non linéaire
Nous construisons un calcul paradifférentiel adapté à l'équation de Schrödinger qui nous permet de montrer un théorème de propagation des singularités pour l'équation de Schrödinger non linéaire en adaptant la méthode de Bony. Nous construisons également la version tangentielle du calcul précédent qui nous permet de montrer un théorème de réflexion transverse des singularités pour l'équation de Schrödinger non linéaire. Nous utilisons alors ce théorème pour calculer l'opérateur...
Propagation of chaos for Burgers' equation
Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
Propagation of electromagnetic waves in non-homogeneous media
We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.
Propagation of Growth Uncertainty in a Physiologically Structured Population
In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described two recent...
Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system.
Propagation of perturbations in thin capillary film equations with nonlinear diffusion and convection.
Propagation of space moments in the Vlasov-Poisson equation and further results
Propagation of uniform Gevrey regularity of solutions to evolution equations
We investigate the propagation of the uniform spatial Gevrey , σ ≥ 1, regularity for t → +∞ of solutions to evolution equations like generalizations of the Euler equation and the semilinear Schrödinger equation with polynomial nonlinearities. The proofs are based on direct iterative arguments and nonlinear Gevrey estimates.
Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations
This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied. This solution...
Proprietà asintotiche delle equazioni di Maxwell nello spazio-tempo di Schwarzschild
Propriétés de la matrice de diffusion, 2-amas 2-amas, pour les problèmes à N corps à longue portée
Propriétés dispersives pour des équations cinétiques et applications à l’équation de Vlasov-Poisson
On considère l’équation de Vlasov-Poisson en dimension 3. On montre des résultats d’existence et d’unicité de solutions faibles de l’équation de Vlasov-Poisson avec densité bornée pour des données initiales ayant strictement moins de six moments dans . La preuve est basée sur une nouvelle approche qui consiste à établir des effets de moments a priori pour des équations de transport avec des termes de force peu réguliers.
Puits de potentiel généralisés et asymptotique semi-classique
Puits multiples en mécanique semi-classique VI. (Cas des puits sous-variétés)
Puits multiples pour l'opérateur de Dirac
Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains
We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality with a large class of non-autonomous external forces. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal...