La première valeur propre du laplacien pour le problème de Dirichlet
Large data local solutions for the derivative NLS equation
We consider the derivative NLS equation with general quadratic nonlinearities. In [2] the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension . Here we prove a similar result for large initial data in all dimensions .
Le problème de Cauchy et la propagation des singularités pour une classe des systèmes hyperboliques non symétrisables
Le problème mixte hyperbolique
Life span of nonnegative solutions to certain quasilinear parabolic Cauchy problems.
Local exact lagrangian controllability of the Burgers viscous equation
Local Existence of Weak Solutions to the Quasi-Linear Wave Equation for Large Initial Values.
Localized minimizers of flat rotating gravitational systems
Longtime behavior of semilinear reaction-diffusion equations on the whole space
Low regularity Cauchy theory for the water-waves problem: canals and swimming pools
The purpose of this talk is to present some recent results about the Cauchy theory of the gravity water waves equations (without surface tension). In particular, we clarify the theory as well in terms of regularity indexes for the initial conditions as fin terms of smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developed in [1, 2], after suitable para-linearizations, the system can be arranged into...
Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system.