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Optimal time decay rates for the compressible Navier-Stokes system with and without Yukawa-type potential. (English) Zbl 1444.35123
Summary: We consider the time decay rates of smooth solutions to the Cauchy problem for the compressible Navier-Stokes system with and without a Yukawa-type potential. We prove the existence and uniqueness of global solutions by the standard energy method under small initial data assumptions. Furthermore, if the initial data belong to $$L^1(\mathbb{R}^3)$$, we establish the optimal time decay rates of the solution as well as its higher-order spatial derivatives. In particular, we obtain the optimal decay rates of the highest-order spatial derivatives of the velocity. Finally, we derive the lower bound time decay rates for the solution and its spacial derivatives.
##### MSC:
 35Q30 Navier-Stokes equations 76N15 Gas dynamics, general
##### Keywords:
compressible flow; energy method; optimal decay rates
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