GLOBAL WELL-POSEDNESS AND DECAY RESULTS FOR 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS IN CRITICAL FOURIER-BESOV-MORREY SPACES

被引：0

作者：

EL Baraka, Azzeddine ^{[1
]}

Toumlilin, Mohamed ^{[1
]}

机构：

[1] Univ Mohamed Ben Abdellah, FST Fes Saiss, Lab AAFA, Dept Math, BP 2202 Route Immouzer, Fes 30000, Morocco

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年

关键词：

2D MHD EQUATIONS; REGULARITY CRITERIA; NAVIER-STOKES; WEAK SOLUTIONS; DISSIPATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory as in [5, 31], we obtain global well-posedness results of the GMHD equations with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover, we prove that the corresponding global solution decays to zero as time approaches infinity.

引用

页数：20

共 37 条

[1]

Bahouri H., 2011, GRUNDLEHREN MATH WIS, V343

[2] Long time decay to the Lei-Lin solution of 3D Navier-Stokes equations [J].

Benameur, Jamel .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 422 (01) :424-434

[3]

Bie Q., 2015, KINETIC RELATED MODE, V8

[4]

Cannone M., 2006, BANACH CTR PUBL, V74, P59

[5] Global well-posedness for Navier-Stokes equations in critical Fourier-Herz spaces [J].

Cannone, Marco ;

Wu, Gang .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (09) :3754-3760

[6] THE 2D INCOMPRESSIBLE MAGNETOHYDRODYNAMICS EQUATIONS WITH ONLY MAGNETIC DIFFUSION [J].

Cao, Chongsheng ;

Wu, Jiahong ;

Yuan, Baoquan .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (01) :588-602

[7] The 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion [J].

Cao, Chongsheng ;

Regmi, Dipendra ;

Wu, Jiahong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (07) :2661-2681

[8] Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion [J].

Cao, Chongsheng ;

Wu, Jiahong .

ADVANCES IN MATHEMATICS, 2011, 226 (02) :1803-1822

[9] Two regularity criteria for the 3D MHD equations [J].

Cao, Chongsheng ;

Wu, Jiahong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (09) :2263-2274

[10] On the Regularity Criterion of Weak Solution for the 3D Viscous Magneto-Hydrodynamics Equations [J].

Chen, Qionglei ;

Miao, Changxing ;

Zhang, Zhifei .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 284 (03) :919-930

← 1 2 3 4 →