Global strong solutions to radial symmetric compressible Navier-Stokes equations bounded by a free surface

被引：0

作者：

Zhang Xingwei ^{[1
]}

机构：

[1] Quzhou Univ, Coll Teacher Educ, Quzhou, Peoples R China

来源：

APPLICABLE ANALYSIS | 2020年 / 99卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Compressible Navier-Stokes equations; free boundary value problem; global strong solution; DEGENERATE VISCOSITY COEFFICIENT; DENSITY-DEPENDENT VISCOSITY; WEAK SOLUTIONS; EXISTENCE; FLOWS;

D O I：

10.1080/00036811.2018.1522629

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the two-dimensional isentropic compressible Navier-Stokes equations bounded by a free surface that is under the surface tension and constant exterior pressure. We establish the existence of global strong solution for arbitrary large spherical initial data with initial density away from the vacuum in the case the viscosity coefficients satisfy . In particular, we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive.

引用

页码：1136 / 1152

页数：17

共 23 条

[1] 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

[2] 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

[3] On compressible Navier-Stokes equations with density dependent viscosities in bounded domains [J].

Bresch, Didier ;

Desjardins, Benoit ;

Gerard-Varet, David .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (02) :227-235

[4] On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids [J].

Bresch, Didier ;

Desjardins, Benoit .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (01) :57-90

[5] On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models [J].

Bresch, Didier ;

Desjardins, Benoit .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2006, 86 (04) :362-368

[6]

Feireisl E., 2004, DYNAMIC VISCOUS COMP

[7] Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients [J].

Guo, Zhenhua ;

Jiu, Quansen ;

Xin, Zhouping .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 39 (05) :1402-1427

[8] Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data [J].

Guo, Zhenhua ;

Wang, Mei ;

Wang, Yi .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 40 :260-289

[9] Lagrange Structure and Dynamics for Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations [J].

Guo, Zhenhua ;

Li, Hai-Liang ;

Xin, Zhouping .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2012, 309 (02) :371-412

[10] Existence and blowup behavior of global strong solutions to the two-dimensional barotrpic compressible Navier-Stokes system with vacuum and large initial data [J].

Huang, Xiangdi ;

Li, Jing .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2016, 106 (01) :123-154

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