Compressible viscous heat-conducting surface wave without surface tension

Abstract

In this paper, we consider a three-dimensional compressible viscous heat-conducting fluid in a horizontally periodic domain, bounded above by a free surface and below by a rigid bottom. The motion of the fluid is governed by the full compressible, gravity-driven Navier–Stokes equations with appropriate boundary conditions. On the free surface, the effect of surface tension is neglected, and the temperature is assumed to satisfy the Robin boundary condition. Motivated by Y. Guo and I. Tice [Anal. PDE 6, 287–369 (2013), Arch. Ration. Mech. Anal. 207, 459–531 (2013), and Anal. PDE 6, 1429–1533 (2013)], we establish the global well-posedness of this free boundary problem, provided that the initial data are close to a nontrivial equilibrium state.