%0 Journal Article
%T Global solution for the 3D gravity water waves system above a flat bottom
%A Xuecheng Wang
%J Mathematics
%D 2015
%I arXiv
%X In this paper, we consider the $3D$ water waves system above a fixed flat bottom (finite depth) with gravity, meanwhile without surface tension (the gravity water waves system). For this system, we prove global existence for suitably small initial data and non-existence of traveling waves below certain level of smallness, which strongly contrasts the behavior of solution of the same system in the $2D$ case.
%U http://arxiv.org/abs/1508.06227v1