Global solution for the 3D gravity water waves system above a flat bottom

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.