Some Estimates of Solutions for the Equations of Motion of Compressible Viscous Fluid in the Three-Dimensional Exterior Domain

We consider the equations of motion of compressible viscous fluid in an exterior domain in 3. We give the Lq−Lp estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem. In particular, we shall give L1 estimates, which implies the diffusion wave of compressible Navier–Stokes flow.