Large-time behaviors of the solution to 3D compressible Navier-Stokes equations in half space with Navier boundary conditions

Teng Wang; Yi Wang

doi:10.3934/cpaa.2021080

Article Contents

2021, Volume 20, Issue 7&8: 2811-2838. Doi: 10.3934/cpaa.2021080

This issue Previous Article Frequency domain approach to decay rates for a coupled hyperbolic-parabolic system Next Article Remarks on global weak solutions to a two-fluid type model

Large-time behaviors of the solution to 3D compressible Navier-Stokes equations in half space with Navier boundary conditions

Teng Wang^1, and
Yi Wang^2,3, ,

1.
College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China
2.
CEMS, HCMS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

^* Corresponding author
^* Corresponding author

Dedicated to Professor Shuxing Chen for his 80th birthday

Received: March 2021

Revised: March 2021

Early access: May 2021

Published: August 2021

The research of T. Wang is partially supported by NSFC grant No. 11971044 and BJNSF grant No. 1202002. The research of Y. Wang is partially supported by the NSFC grants No. 12090014 and 11688101.

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Abstract

We are concerned with the large-time asymptotic behaviors towards the planar rarefaction wave to the three-dimensional (3D) compressible and isentropic Navier-Stokes equations in half space with Navier boundary conditions. It is proved that the planar rarefaction wave is time-asymptotically stable for the 3D initial-boundary value problem of the compressible Navier-Stokes equations in $ \mathbb{R}^+\times \mathbb{T}^2 $ with arbitrarily large wave strength. Compared with the previous work [17, 16] for the whole space problem, Navier boundary conditions, which state that the impermeable wall condition holds for the normal velocity and the fluid tangential velocity is proportional to the tangential component of the viscous stress tensor on the boundary, are crucially used for the stability analysis of the 3D initial-boundary value problem.

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Mathematics Subject Classification: Primary: 35M33 35Q30 76N06; Secondary: 76N30 76E30.

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