Jean-Yves Chemin

Remarques sur l'apparition de singularités dans les écoulements eulériens compressibles

We recall some basic facts about the breakdown of smoothness in general hyperbolic systems and then, we prove that the breakdown of smoothness in an Euclidean flow comes from an accumulation of vorticity, divergence or compression.

The Role of Spectral Anisotropy in the Resolution of the Three-Dimensional Navier–Stokes Equations

We present different classes of initial data to the three-dimensional, incompressible Navier–Stokes equations, which generate a global in time, unique solution though they may be arbitrarily large in the endpoint function space in which a fixed-point argument may be used to solve the equation locally in time. The main feature of these initial data is an anisotropic distribution of their frequencies. One of those classes is taken from Chemin and Gallagher (Trans. Am. Math. Soc. 362(6):2859–2873, 2010) and Chemin et al. (J. fur die reine und angewandte Mathematik, to appear), and another one is new.

Analyse microlocale et mécanique des fluides en dimension deux

Dans ce texte, nous avons cherche a donner un apercu sur quelques resultats recents demontres sur l’equation d’Euler incompressible en dimension deux. Nous avons voulu mettre l’accent sur l’importance que peuvent prendre l’aspect geometrique et les idees venues de l’analyse microlocale dans la description precise de la regularite des solutions du systeme d’Euler.