Recent progress on classical solutions for compressible isentropic Navier-Stokes equations with degenerate viscosities and vacuum

被引：16

作者：

Li, Yachun ^{[1
,2
]}

Pan, Ronghua ^{[3
]}

Zhu, Shengguo ^{[3
,4
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China

[3] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[4] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2016年 / 47卷 / 02期

基金：

美国国家科学基金会; 上海市自然科学基金; 中国国家自然科学基金;

关键词：

Navier-Stokes; vacuum; degenerate viscosity; regular solutions; blowup; GLOBAL SMOOTH SOLUTIONS; BLOW-UP; EULER EQUATIONS; WEAK SOLUTIONS; EXISTENCE; FLUIDS; DENSITY; FLOWS;

D O I：

10.1007/s00574-016-0165-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to present our recent progress on the local theory of classical solutions for compressible isentropic Navier-Stokes equations with density dependent viscosities in a power law and vacuum, which is a long-standing open problem due to the very high degeneracy caused by vacuum for this system. We will also mention some related open problems of high mathematical interest for this system.

引用

页码：507 / 519

页数：13

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