Inflow problem for the one-dimensional compressible Navier-Stokes equations under large initial perturbation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

Fan, Lili¹  Liu, Hongxia²  Wang, Tao³  Zhao, Huijiang³ 

[1] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China

[2] Jinan Univ, Dept Math, Guangzhou 510632, Guangdong, Peoples R China

[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

关键词: Compressible Navier-Stokes equations;    Boundary layer solution;    Inflow problem;    Rarefaction wave;    Large initial perturbation;    Large density oscillation;   

DOI  :  10.1016/j.jde.2014.07.001

来源: Elsevier

【 摘 要 】

This paper is concerned with the inflow problem for the one-dimensional compressible Navier-Stokes equations. For such a problem, Matsumura and Nishihara showed in [10] that there exists boundary layer solution to the inflow problem, and that both the boundary layer solution, the rarefaction wave, and the superposition of boundary layer solution and rarefaction wave are nonlinear stable under small initial perturbation. The main purpose of this paper is to show that similar stability results for the boundary layer solution and the supersonic rarefaction wave still hold for a class of large initial perturbation which can allow the initial density to have large oscillation. The proofs are given by an elementary energy method and the key point is to deduce the desired lower and upper bounds on the density function. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free