ASYMPTOTIC BEHAVIOR OF THE STOKES APPROXIMATION EQUATIONS FOR COMPRESSIBLE FLOWS IN R3

doi:10.1016/S0252-9602(15)30018-7

Abstract

Abstract:

We consider the Stokes approximation equations for compressible flows in R³. The global unique solution and optimal convergence rates are obtained by pure energy method provided the initial perturbation around a constant state is small. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. As an immediate byproduct, the usual L^p-L²(1≤ p≤ 2) type of the optimal decay rate follow without requiring that the L^p norm of initial data is small.

Key words: Stokes approximation equations, energy method, optimal decay rates, Sobolev interpolation, negative Sobolev space

CLC Number:

35B40

Yunshun WU, Zhong TAN. ASYMPTOTIC BEHAVIOR OF THE STOKES APPROXIMATION EQUATIONS FOR COMPRESSIBLE FLOWS IN R³[J].Acta mathematica scientia,Series B, 2015, 35(3): 746-760.

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ASYMPTOTIC BEHAVIOR OF THE STOKES APPROXIMATION EQUATIONS FOR COMPRESSIBLE FLOWS IN R³

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