Global strong solutions to the 3D incompressible MHD equations with density-dependent viscosity

被引：10

作者：

Yu, Haibo ^{[1
]}

Zhang, Peixin ^{[1
]}

Shi, Xiujuan ^{[2
]}

机构：

[1] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China

[2] Yang En Univ, Dept Math, Quanzhou 362014, Fujian, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 08期

基金：

中国博士后科学基金;

关键词：

Global strong solution; Incompressible MHD equations; Density-dependent viscosity; Vacuum; NAVIER-STOKES EQUATIONS; MIXED PARTIAL DISSIPATION; BOUNDARY-VALUE PROBLEM; MAGNETIC DIFFUSION; WELL-POSEDNESS; REGULARITY; FLUIDS; SOLVABILITY; EXISTENCE; SYSTEM;

D O I：

10.1016/j.camwa.2018.01.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the 3D incompressible MHD equations with density dependent viscosity in smooth bounded domains. Through time-weighted a priori estimates, the global existence of strong solutions is established under the assumption that the initial energy is suitably small. This generalizes previous results for the 3D Navier-Stokes equations in Huang and Wang (2015) and Zhang (2015), which need II Vuollo to be small. The initial vacuum is allowed. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：2825 / 2834

页数：10

共 28 条

[1] [Anonymous], 1994, Springer Tracts in Natural Philosophy
[2] Antontsev S. A., 1973, Mathematical Study of Flows of Nonhomogeneous Fluids
[3] Antontsev SN, 1989, BOUNDARY VALUE PROBL
[4] Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
Cao, Chongsheng
Wu, Jiahong
[J]. ADVANCES IN MATHEMATICS, 2011, 226 (02) : 1803 - 1822
[5] On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
Cho, YG
Kim, H
[J]. MANUSCRIPTA MATHEMATICA, 2006, 120 (01) : 91 - 129
[6] Unique solvability for the density-dependent Navier-Stokes equations
Cho, YG
Kim, HS
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 59 (04) : 465 - 489
[7] Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids
Choe, HJ
Kim, H
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (5-6) : 1183 - 1201
[8] Global Wellposedness for the 3D Inhomogeneous Incompressible Navier-Stokes Equations
Craig, Walter
Huang, Xiangdi
Wang, Yun
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2013, 15 (04) : 747 - 758
[9] Regularity results for two-dimensional flows of multiphase viscous fluids
Desjardins, B
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 137 (02) : 135 - 158
[10] Desjardins B., 1998, Differ. Integral Equ., V11, P377

← 1 2 3 →