Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain

被引：58

作者：

Dou, Changsheng ^{[1
]}

Jiang, Song ^{[2
]}

Ou, Yaobin ^{[3
]}

机构：

[1] Capital Univ Econ & Business, Sch Stat, Beijing 100070, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[3] Renmin Univ China, Sch Informat, Beijing 100872, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 258卷 / 02期

关键词：

Low Mach number limit; Full Navier-Stokes equations; Slip boundary conditions; Bounded domain; Polytropic gas; INCOMPRESSIBLE LIMIT; COMPRESSIBLE FLOWS; SINGULAR LIMITS;

D O I：

10.1016/j.jde.2014.09.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional bounded domain where the velocity field and the temperature satisfy the slip boundary conditions and the Neumann boundary condition, respectively. The uniform estimates in the Mach number for the strong solutions are derived in a short time interval, provided that the initial density and temperature are close to the constant states and satisfy the "bounded derivative conditions". Thus the solutions of the full compressible Navier-Stokes equations converge to the one of the isentropic incompressible Navier-Stokes equations, as the Mach number vanishes. (C) 2014 Published by Elsevier Inc.

引用

页码：379 / 398

页数：20

共 28 条

[1] Low mach number limit of the full Navier-Stokes equations [J].

Alazard, T .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2006, 180 (01) :1-73

[2]

Alazard T, 2005, ADV DIFFERENTIAL EQU, V10, P19

[3]

Bourguignon J. P., 1974, J. Functional Analysis, V15, P341

[4] Low Mach number limit of viscous polytropic flows: Formal asymptotics in the periodic case [J].

Bresch, D ;

Desjardins, B ;

Grenier, E ;

Lin, CK .

STUDIES IN APPLIED MATHEMATICS, 2002, 109 (02) :125-149

[5] Zero Mach number limit for compressible flows with periodic boundary conditions [J].

Danchin, R .

AMERICAN JOURNAL OF MATHEMATICS, 2002, 124 (06) :1153-1219

[6] SINGULAR LIMITS IN COMPRESSIBLE FLUID-DYNAMICS [J].

DAVEIGA, HB .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1994, 128 (04) :313-327

[7] Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions [J].

Desjardins, B ;

Grenier, E ;

Lions, PL ;

Masmoudi, N .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1999, 78 (05) :461-471

[8] Low Mach number limit of viscous compressible flows in the whole space [J].

Desjardins, B ;

Grenier, E .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 455 (1986) :2271-2279

[9] On the incompressible limit for the Navier-Stokes-Fourier system in domains with wavy bottoms [J].

Feireisl, Eduard ;

Novotny, Antonin ;

Petzeltova, Hana .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (02) :291-324

[10] The low mach number limit for the full navier-stokes-fourier system [J].

Feireisl, Eduard ;

Novotny, Antonin .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 186 (01) :77-107

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