Global existence and decay estimate of classical solutions to the compressible viscoelastic flows with self-gravitating

Yinxia Wang; Hengjun Zhao

doi:10.3934/cpaa.2018020

Article Contents

2018, Volume 17, Issue 2: 347-374. Doi: 10.3934/cpaa.2018020

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Global existence and decay estimate of classical solutions to the compressible viscoelastic flows with self-gravitating

Yinxia Wang^1, and
Hengjun Zhao^2,

1.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China
2.
College of Sciences, Henan University of Engineering, Zhengzhou, 451191, China

Received: January 31, 2017

Revised: March 31, 2017

Published: June 2018

YXW is supported by NNSF grant No.11101144.

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Abstract

In this paper, we consider the initial value problem for the compressible viscoelastic flows with self-gravitating in $\mathbb{R}^n(n≥ 3)$. Global existence and decay rates of classical solutions are established. The corresponding linear equations becomes two similar equations by using Hodge decomposition and then the solutions operator is derived. The proof is mainly based on the decay properties of the solutions operator and energy method. The decay properties of the solutions operator may be derived from the pointwise estimate of the solution operator to two linear wave equations.

Keywords:

Compressible viscoelastic flows with self-gravitating,
global classical solution,
decay rates.

Mathematics Subject Classification: Primary:35B40;Secondary:76N15.

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