DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.29, no.3, pp.769 - 801
Abstract
In this paper, we study the incompressible Navier-Stokes equations on a moving domain in R(3) of finite depth, bounded above by the free surface and bounded below by a solid flat bottom. We prove that there exists a unique, global-in-time solution to the problem provided that the initial velocity field and the initial profile of the boundary are sufficiently small in Sobolev spaces