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

Abstract

Given any suitably small, localized, and smooth initial data, in this paper, we prove global regularity for the $3D$ finite depth gravity water wave system. As a byproduct, we rule out the small, localized traveling waves in $3D$, which do exist for the same system in $2D$.

Published version

References in corpus (2)

• Decay estimates for a class of wave equations
• Global analysis of a model for capillary water waves in 2D

Cited by in corpus (3)

• Long-time existence for multi-dimensional periodic water waves
• Integral and asymptotic properties of solitary waves in deep water
• On the mathematical description of time-dependent surface water waves