The main result of this talk is a global existence theorem for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution, which shows that modified scattering holds.
The proof is based on a bootstrap argument involving and estimates. The bounds are proved in the paper [5]. They rely on a normal forms paradifferential method allowing one to obtain energy estimates on the...
Le résultat principal de cet exposé énonce que le problème de Cauchy pour les équations adimensionnées d’un fluide général est bien posé sur un intervalle de temps indépendant des nombres de Mach, Reynolds et Péclet.
In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system with surface tension. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [3]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at ()).
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