The initial-boundary value problem for the compressible viscoelastic flows

Xianpeng Hu; Dehua Wang

doi:10.3934/dcds.2015.35.917

Article Contents

2015, Volume 35, Issue 3: 917-934. Doi: 10.3934/dcds.2015.35.917

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The initial-boundary value problem for the compressible viscoelastic flows

Xianpeng Hu^1, and
Dehua Wang^2,

1.
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
2.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Received: February 28, 2014

Revised: February 28, 2014

Published: February 2015

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Abstract

The initial-boundary value problem for the equations of compressible viscoelastic flows is considered in a bounded domain of three-dimensional spatial dimensions. The global existence of strong solution near equilibrium is established. Uniform estimates in $W^{1,q}$ with $q>3$ on the density and deformation gradient are also obtained.

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Mathematics Subject Classification: 35A05, 76A10, 76D03.

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