Local well-posedness in critical spaces for the compressible MHD equations

被引：6

作者：

Bian, Dongfen ^{[1
,2
]}

Yuan, Baoquan ^{[1
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454000, Henan, Peoples R China

[2] China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R China

来源：

APPLICABLE ANALYSIS | 2016年 / 95卷 / 02期

基金：

中国国家自然科学基金;

关键词：

compressible MHD equations; Besov spaces; critical spaces; Littlewood-Paley theory; local well-posedness; NAVIER-STOKES EQUATIONS; SHALLOW-WATER EQUATIONS; HEAT-CONDUCTIVE GASES/; GLOBAL EXISTENCE; VISCOUS FLUIDS; CAUCHY-PROBLEM; DENSITY; FLOW;

D O I：

10.1080/00036811.2014.910651

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove local well-posedness in critical Besov spaces for the compressible MHD equations in R-N,R- N >= 2, under the assumptions that the initial density is bounded above and bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.

引用

页码：239 / 269

页数：31

共 29 条

[11] Global existence in critical spaces for compressible Navier-Stokes equations
Danchin, R
[J]. INVENTIONES MATHEMATICAE, 2000, 141 (03) : 579 - 614
[12] Well-posedness in critical spaces for barotropic viscous fluids with truly not constant density
Danchin, R.
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1373 - 1397
[13] On the uniqueness in critical spaces for compressible Navier-Stokes equations
Danchin, R
[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2005, 12 (01): : 111 - 128
[14] Density-dependent incompressible viscous fluids in critical spaces
Danchin, R
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2003, 133 : 1311 - 1334
[15] Global existence in critical spaces for flows of compressible viscous and heat-conductive gases
Danchin, R
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 160 (01) : 1 - 39
[16] Local theory in critical spaces for compressible viscous and heat-conductive gases
Danchin, R
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (7-8) : 1183 - 1233
[17] ON THE NAVIER-STOKES INITIAL VALUE PROBLEM .1.
FUJITA, H
KATO, T
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1964, 16 (04) : 269 - 315
[18] CAUCHY PROBLEM FOR VISCOUS SHALLOW WATER EQUATIONS WITH A TERM OF CAPILLARITY
Haspot, Boris
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2010, 20 (07) : 1049 - 1087
[19] MULTIDIMENSIONAL DIFFUSION WAVES FOR THE NAVIER-STOKES EQUATIONS OF COMPRESSIBLE FLOW
HOFF, D
ZUMBRUN, K
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1995, 44 (02) : 603 - 676
[20] ITAYA N., 1976, J. Math. Kyoto Univ., V16, P413, DOI [10.1215/kjm/1250522922, DOI 10.1215/KJM/1250522922]

← 1 2 3 →