ASYMPTOTIC BEHAVIOR OF THE LINEARIZED PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE SURFACE

Deriving from the motion of a three-dimensional compressible viscous heat -conducting fluid in an infinite layer bounded above by a free surface, the paper is concerned with the asymptotic behavior of solutions to the linearized compressible Navier-Stokes equations in a strip domain. With the help of the explicit solution formula for the corresponding resolvent problem we have achieved, the time -decay estimates of solutions to this problem in L-p spaces, 2 <= p < infinity, are well established. Moreover, since we are interested in the linearized dynamic boundary condition of the surface wave problem, some exponential decay properties of the solutions are revealed. Our result is crucial and indispensable for developing the L-p theory for the free boundary problem of the full compressible Navier-Stokes equations.