Decay of the compressible viscoelastic flows

W. Wei; Yin  Li; Zheng-An Yao

doi:10.3934/cpaa.2016004

Article Contents

2016, Volume 15, Issue 5: 1603-1624. Doi: 10.3934/cpaa.2016004

This issue Previous Article Scattering for a nonlinear Schrödinger equation with a potential Next Article Multiplicity of subharmonic solutions and periodic solutions of a particular type of super-quadratic Hamiltonian systems

Decay of the compressible viscoelastic flows

1.
Department of Mathematics, Guizou University, Guiyang, Guizhou Province
2.
School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005
3.
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275

Received: December 2014

Revised: May 2016

Published: September 2016

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Abstract

In this paper we study the time decay rates of the solution to the Cauchy problem for the compressible viscoelastic flows via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, and the $\dot{H}^{-s}(0\leq s<\frac{3}{2})$ negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 76N15, 76P05, 82C40.

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