Stability of boundary layer and rarefaction wave to an outflow problem for compressible Navier-Stokes equations under large perturbation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Huang, Feimin²  Qin, Xiaohong¹ 

[1] Nanjing Univ Sci & Technol, Dept Math, Nanjing 210094, Peoples R China

[2] Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China

关键词: Compressible Navier-Stokes equations;    Stability;    Boundary layer;    Rarefaction wave;    Urge perturbation;   

DOI  :  10.1016/j.jde.2009.01.017

来源: Elsevier

【 摘 要 】

In this paper, we investigate the large-time behavior of solutions to an outflow problem for compressible Navier-Stokes equations. In 2003, Kawashima, Nishibata and Zhu [S. Kawashima, S. Nishibata, R Zhu, Asymptotic stability of the stationary Solution to the compressible Navier-Stokes equations in the half space, Comm. Math. Phys. 240 (2003) 483-500] showed there exists a boundary layer (i.e., stationary solution) to the Outflow problem and the boundary layer is nonlinearly stable under small initial perturbation. In the present paper, we show that not only the boundary layer above but also the superposition of a boundary layer and a rarefaction wave are stable under large initial perturbation. The proofs are given by an elementary energy method. (C) 2009 Elsevier Inc. All rights reserved.

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