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

Abstract We consider the equations of motion of compressible viscous fluid in an exterior domain in R 3 . We give the L q − L p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem. In particular, we shall give L 1 estimates, which implies the diffusion wave of compressible Navier–Stokes flow.