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Some estimates of solutions for the equations of motion of compressible viscous fluid in the three-dimensional exterior domain. (English) Zbl 1069.35051
Summary: We consider the equations of motion of a compressible viscous fluid in an exterior domain in $$\mathbb R^3$$. 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 give $$L_1$$ estimates, which implies the diffusion wave of compressible Navier-Stokes flow.

##### MSC:
 35Q30 Navier-Stokes equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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##### References:
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