Solvability of the free boundary value problem of the Navier-Stokes equations
Solvability of the free boundary value problem of the Navier-Stokes equations
In this paper, we study the incompressible Navier-Stokes equations on a moving domain in $\mathbb{R}^{3}$ 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 …