A survey of the compressible Navier-Stokes equations

被引：20

作者：

Desjardins, B

Lin, CK

机构：

[1] Ecole Normale Super, Dept Math & Informat, F-75005 Paris, France

[2] Natl Cheng Kung Univ, Dept Math, Tainan 70001, Taiwan

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 1999年 / 3卷 / 02期

关键词：

global weak solution; regularity; blow up; compressibility; viscosity; entropy; incompressible limit;

D O I：

10.11650/twjm/1500407089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper presents mathematical properties of solutions to the Navier-Stokes equations for compressible fluids. We first review existence results for the Cauchy problem, and describe some regularity properties of solutions in the presence of possibly vanishing densities. Finally, we address the problem of the low Mach number limit leading to incompressible models.

引用

页码：123 / 137

页数：15

共 50 条

[1] Convergence of the relaxed compressible Navier-Stokes equations to the incompressible Navier-Stokes equations
Ju, Qiangchang
Wang, Zhao
[J]. APPLIED MATHEMATICS LETTERS, 2023, 141
[2] DEFICIENCY OF COMPRESSIBLE, NAVIER-STOKES EQUATIONS
GORDON, P
[J]. SIAM REVIEW, 1973, 15 (01) : 253 - &
[3] On the barotropic compressible Navier-Stokes equations
Mellet, A.
Vasseur, A.
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (03) : 431 - 452
[4] Hyperbolic compressible Navier-Stokes equations
Hu, Yuxi
Racke, Reinhard
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (04) : 3196 - 3220
[5] A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
Danchin, Raphael
[J]. SCIENCE CHINA-MATHEMATICS, 2012, 55 (02) : 245 - 275
[6] A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
Raphaël Danchin
[J]. Science China Mathematics, 2012, 55 : 245 - 275
[7] A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
DANCHIN Raphaёl
[J]. Science China Mathematics, 2012, 55 (02) : 245 - 275
[8] Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations
YANG JianWei
WANG Shu
[J]. Science China Mathematics, 2014, 57 (10) : 2153 - 2162
[9] Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations
JianWei Yang
Shu Wang
[J]. Science China Mathematics, 2014, 57 : 2153 - 2162
[10] Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations
Yang JianWei
Wang Shu
[J]. SCIENCE CHINA-MATHEMATICS, 2014, 57 (10) : 2153 - 2162

← 1 2 3 4 5 →