Titre : Non uniform rotating vortices for the Euler equations
Résumé : The motion of a uniform incompresible ideal fluid can be described through the Euler equations. In this talk, some special solutions will be introduced: stationary, translating and rotating solutions. A vortex patch is a solution that is uniformly supported in a bounded domain (which evolves with the time). There are recent works dealing with the existence of periodic vortex patches, which are obtained by perturbing the circular patch (which is stationary). Using similar techniques, i.e. the bifurcation theory, our goal is to find non uniform periodic solutions for the Euler equations. This is a joint work with T. Hmidi and J. Soler.