Global well-posedness of the free-surface incompressible Euler equations with damping

Abstract

We consider a layer of an incompressible inviscid fluid, bounded below by a fixed solid boundary and above by a free moving boundary, in a horizontally periodic setting. The fluid dynamics is governed by the gravity-driven incompressible Euler equations with damping, and the effect of surface tension is neglected on the free surface. We prove that the problem is globally well-posed for the small initial data and that solutions decay to the equilibrium at an almost exponential rate.