Global infinite energy solutions for the 2D gravity water waves system

Abstract

We prove global existence and modified scattering property for the solutions of the $2D$ gravity water waves system in the infinite depth setting for a class of initial data, which is only required to be small above the level ${\dot{H}}^{1/5}\times {\dot{H}}^{1/5+1/2}$. No assumption is assumed below this level, therefore, it allows to have infinite energy. As a direct consequence, the momentum condition assumed on the physical velocity in all previous small energy results by Ionescu-Pusateri, Alazard-Delort and Ifrim-Tataru is removed.

Revised version

References in corpus (2)

• Two dimensional water waves in holomorphic coordinates
• Global analysis of a model for capillary water waves in 2D