Stability of the composite wave for the inflow problem on the micropolar fluid model

Haibo Cui; Haiyan Yin

doi:10.3934/cpaa.2017062

Article Contents

2017, Volume 16, Issue 4: 1265-1292. Doi: 10.3934/cpaa.2017062

This issue Previous Article Hardy-Sobolev type integral systems with Dirichlet boundary conditions in a half space Next Article Robin problems with indefinite linear part and competition phenomena

Stability of the composite wave for the inflow problem on the micropolar fluid model

Haibo Cui^1, and
Haiyan Yin^2, ,

1.
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
2.
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

^* Corresponding author: yinhaiyan2000@aliyun.com
^* Corresponding author: yinhaiyan2000@aliyun.com

Received: June 30, 2016

Revised: January 31, 2017

Published: May 2017

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Abstract

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in half line $\mathbb{R}_{+}:=(0, \infty).$ Inspired by the relationship between the micropolar fluid model and Navier-Stokes system, we can prove that the composite wave consisting of the subsonic BL-solution, the contact wave, and the rarefaction wave for the inflow problem on micropolar fluid model is time-asymptotically stable. Meanwhile, we obtain the global existence of solutions based on the basic energy method.

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Mathematics Subject Classification: Primary: 35Q35, 76D33; Secondary: 35M33, 35B35.

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