We consider the global stability of the compressible viscous surface waves in the
absence of surface tension effect with steady-state configurations and the reference
domain being the horizontal infinite layer. The fluid dynamics are governed by the
three-dimensional gravity-driven isentropic compressible Navier–Stokes equations. We
develop a new mathematical approach to establish global well-posedness of free
boundary problems of the multidimensional compressible Navier–Stokes system based
on the Lagrangian framework, which requires no compatibility conditions on the
initial data.
Keywords
compressible viscous surface waves, Lagrangian coordinates,
global well-posedness, steady-state
