Existence of threedimensional, steady, inviscid, incompressible flows with nonvanishing vorticity.
Existence of time-periodic solutions to incompressible Navier-Stokes equations in the whole space.
Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
Existence of weak solutions for a nonhomogeneous solidification mathematical model.
Existence of weak solutions for a nonlinear elliptic system.
Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow.
Existence of weak solutions for quasilinear elliptic equations involving the -Laplacian.
Existence of weak solutions for the thermistor problem with degeneracy.
Existence of weak solutions to a class of degenerate semiconductor equations modeling avalanche generation.
Existence results for a nonlinear problem modeling the displacement of a solid in a transverse flow
Existence results for mean field equations
Existence results for the flow of viscoelastic fluids of White-Metzner type.
This work is concerned with the study of the flow of an incompressible viscoelastic fluid of White-Metzner type. These models lead to systems of partial differential equations that are evolutionary, are globally well posed. The objective of this article is to prove the local and global existence of solutions of these systems.
Existence, uniqueness and attainability of periodic solutions of the Navier-Stokes equations in exterior domains
Existence, uniqueness, and quasilinearization results for nonlinear differential equations arising in viscoelastic fluid flow.
Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in
For a bounded domain , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system , , with , , and very general data classes for , , such that may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...
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.