VANISHING VISCOSITY LIMIT TO RAREFACTION WAVES FOR THE FULL COMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE

被引：8

作者：

Wang, Wenjun ^{[1
]}

Yao, Lei ^{[2
,3
]}

机构：

[1] Shanghai Univ Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[2] Northwest Univ, Sch Math, Xian 710127, Peoples R China

[3] Northwest Univ, Ctr Nonlinear Studies, Xian 710127, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes-Korteweg system; rarefaction wave; vanishing viscosity limit; L-2 energy estimate; NAVIER-STOKES EQUATIONS; ZERO DISSIPATION LIMIT; NONLINEAR STABILITY; EXISTENCE; SYSTEM;

D O I：

10.3934/cpaa.2014.13.2331

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the solution of the full compressible fluid models of Korteweg type with centered rarefaction wave data of large strength exists globally in time. As the viscosity, heat-conductivity and capillary coefficients tend to zero, the global solution converges to the centered rarefaction wave solution of the corresponding Euler equations uniformly when the initial perturbation is small. Our analysis is based on the energy method.

引用

页码：2331 / 2350

页数：20

共 22 条

[1] On some compressible fluid models: Korteweg, lubrication, and shallow water systems [J].

Bresch, D ;

Desjardins, B ;

Lin, CK .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (3-4) :843-868

[2] Existence and nonlinear stability of stationary solutions to the full compressible Navier-Stokes-Korteweg system [J].

Chen, Zhengzheng ;

Zhao, Huijiang .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2014, 101 (03) :330-371

[3] Nonlinear stability of viscous contact wave for the one-dimensional compressible fluid models of Korteweg type [J].

Chen, Zhengzheng ;

Xiao, Qinghua .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (17) :2265-2279

[4] Asymptotic stability of strong rarefaction waves for the compressible fluid models of Korteweg type [J].

Chen, Zhengzheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 394 (01) :438-448

[5] Existence of solutions for compressible fluid models of Korteweg type [J].

Danchin, R ;

Desjardins, B .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2001, 18 (01) :97-133

[6]

DUNN JE, 1985, ARCH RATION MECH AN, V88, P95

[7] Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type [J].

Haspot, Boris .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2011, 13 (02) :223-249

[8] SOLUTIONS FOR 2-DIMENSIONAL SYSTEM FOR MATERIALS OF KORTEWEG TYPE [J].

HATTORI, H ;

LI, DN .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1994, 25 (01) :85-98

[9]

Hattori H., 1996, J. Partial Differ. Equ, V9, P323

[10] Global solutions of a high dimensional system for Korteweg materials [J].

Hattori, HHH ;

Li, DN .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 198 (01) :84-97

← 1 2 3 →