ASYMPTOTIC LIMIT OF A NAVIER-STOKES-KORTEWEG SYSTEM WITH DENSITY-DEPENDENT VISCOSITY

被引：2
作者：
Yang, Jianwei [1 ]
Cheng, Peng [1 ]
Wang, Yudong [1 ]
机构：
[1] North China Univ Water Resources & Elect Power, Coll Math & Informat Sci, Zhengzhou 450045, Henan Province, Peoples R China
来源：
ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES | 2015年 / 22卷
基金：
中国国家自然科学基金;
关键词：
Incompressible limit; vanishing capillarity limit; modulated energy; Navier-Stokes-Korteweg model; incompressible Navier-Stokes equations; COMPRESSIBLE FLUID MODELS; GLOBAL WEAK SOLUTIONS; DECAY-RATE; EXISTENCE; EQUATIONS; CONVERGENCE; DYNAMICS;
D O I：
10.3934/era.2015.22.20
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study a combined incompressible and vanishing capillarity limit in the barotropic compressible Navier-Stokes-Korteweg equations for weak solutions. For well prepared initial data, the convergence of solutions of the compressible Navier-Stokes-Korteweg equations to the solutions of the incompressible Navier-Stokes equation are justified rigorously by adapting the modulated energy method. Furthermore, the corresponding convergence rates are also obtained.
引用
收藏
页码：20 / 31
页数：12
相关论文
共 30 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]  
[Anonymous], 1901, ARCH NEERL SCI EXACT
[3]  
[Anonymous], 1894, Z. Phys. Chem., DOI [10.1515/zpch-1894-1338, DOI 10.1515/ZPCH-1894-1338]
[4]  
Benzoni-Gavage S, 2006, ELECTRON J DIFFER EQ
[5]   Convergence of the Vlasov-Poisson system to the incompressible Euler equations [J].
Brenier, Y .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (3-4) :737-754
[6]   Quasi-neutral limit for a viscous capillary model of plasma [J].
Bresch, D ;
Desjardins, B ;
Ducomet, B .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2005, 22 (01) :1-9
[7]   Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model [J].
Bresch, D ;
Desjardins, B .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 238 (1-2) :211-223
[8]   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
[9]   EXISTENCE OF A GLOBAL STRONG SOLUTION AND VANISHING CAPILLARITY-VISCOSITY LIMIT IN ONE DIMENSION FOR THE KORTEWEG SYSTEM [J].
Charve, Frederic ;
Haspot, Boris .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (02) :469-494
[10]   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
123