Strong solutions to compressible barotropic viscoelastic flow with vacuum

Tong  Tang; Yongfu  Wang

doi:10.3934/krm.2015.8.765

Article Contents

2015, Volume 8, Issue 4: 765-775. Doi: 10.3934/krm.2015.8.765

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Strong solutions to compressible barotropic viscoelastic flow with vacuum

Tong Tang^1, and
Yongfu Wang^2,

1.
Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098
2.
Department of Mathematics, Sichuan University, Chengdu, 610064

Received: October 31, 2014

Revised: April 30, 2015

Published: November 2015

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Abstract

We consider strong solutions to compressible barotropic viscoelastic flow in a domain $\Omega\subset\mathbb{R}^{3}$ and prove the existence of unique local strong solutions for all initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Inspired by the work of Kato and Lax, we use the contraction mapping principle to get the result.

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Mathematics Subject Classification: Primary: 35Q35, 76A10, 76N10.

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