Existence and stability of stationary solution to compressible Navier-Stokes-Poisson equations in half line

被引：13

作者：

Wang, Lei ^{[1
]}

Zhang, Guojing ^{[1
]}

Zhang, Kaijun ^{[1
]}

机构：

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 145卷

基金：

美国国家科学基金会;

关键词：

Compressible Navier-Stokes-Poisson equation; Outflow problem; Boundary layer; Asymptotic stability; Convergence rate; Weighted energy estimates; ASYMPTOTIC STABILITY; RAREFACTION WAVE; CONVERGENCE RATE; P-SYSTEM; SPACE; BOUNDARY;

D O I：

10.1016/j.na.2016.08.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the asymptotic stability of the stationary solution to the outflow problem for the compressible Navier-Stokes-Poisson system in a half line. We show the existence of the stationary solution with the aid of the stable manifold theory. The time asymptotic stability of the stationary solution is obtained by the elementary energy method. Furthermore, for the supersonic flow at spatial infinity, we also obtain an algebraic and an exponential decay rate, when the initial perturbation belongs to the corresponding weighted Sobolev space. The proof is based on a time and space weighted energy method. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：97 / 117

页数：21

共 26 条

[1] On the Nonexistence of Global Weak Solutions to the Navier-Stokes-Poisson Equations in N [J].

Chae, Dongho .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (03) :535-557

[2]

Degond P., 2000, AMS/IP Stud. Adv. Math., V266, P77

[3] A quasineutral type limit for the Navier-Stokes-Poisson system with large data [J].

Donatelli, D. ;

Marcati, P. .

NONLINEARITY, 2008, 21 (01) :135-148

[4] Local and global existence for the coupled Navier-Stokes-Poisson problem [J].

Donatelli, D .

QUARTERLY OF APPLIED MATHEMATICS, 2003, 61 (02) :345-361

[5] STABILITY OF RAREFACTION WAVE AND BOUNDARY LAYER FOR OUTFLOW PROBLEM ON THE TWO-FLUID NAVIER-STOKES-POISSON EQUATIONS [J].

Duan, Renjun ;

Yang, Xiongfeng .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (02) :985-1014

[6] Global existence for compressible Navier-Stokes-Poisson equations in three and higher dimensions [J].

Hao, Chengchun ;

Li, Hai-Liang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (12) :4791-4812

[7]

Hsiao L, 2010, ACTA MATH SCI, V30, P1937

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

Huang, Feimin ;

Qin, Xiaohong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (10) :4077-4096

[9] Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space [J].

Kagei, Yoshiyuki ;

Kawashima, Shuichi .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 266 (02) :401-430

[10] Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space [J].

Kawashima, S ;

Nishibata, S ;

Zhu, PC .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 240 (03) :483-500

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