Optimal Time Decay Rates for the Compressible Navier-Stokes System with and Without Yukawa-type Potential
Electronic journal of differential equations(2020)
Abstract
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 (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.
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Key words
Compressible flow,energy method,optimal decay rates
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