On global existence, energy decay and blow-up criteria for the Hall-MHD system

被引：99

作者：

Wan, Renhui ^{[1
]}

Zhou, Yong ^{[2
,3
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China

[3] King Abdulaziz Univ, Fac Sci, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 11期

关键词：

Hall-MHD system; Global well-posedness; Energy decay; Blow-up criteria; WELL-POSEDNESS; WEAK SOLUTIONS;

D O I：

10.1016/j.jde.2015.07.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we obtain global existence and energy decay for 3D Hall-magnetohydrodynamics (Hall-MHD) system with Ait and AB. Besides the classical energy method and Besov space techniques, the interpolating inequalities are crucial in the proof of decay estimates. Then two Osgood type blow-up criteria are established. Our results improve the corresponding theorems in 3 and M. In addition, we establish two Beale Kato Majda blow-up criterion for the generalized version of Hall-MHD with -Delta u and (-Delta)beta B, beta>1. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：5982 / 6008

页数：27

共 18 条

[1] KINETIC FOR MULATION AND GLOBAL EXISTENCE FOR THE HALL-MAGNETO-HYDRODYNAMICS SYSTEM [J].

Acheritogaray, Marion ;

Degond, Pierre ;

Frouvelle, Amic ;

Liu, Jian-Guo .

[2]

Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1

[3]

Benvenutti M., ARXIV14128516V1

[4]

Chae D., 2015, ANN I H POI IN PRESS

[5]

Chae D., ARXIV14040486V2

[6] Well-posedness for Hall-magnetohydrodynamics [J].

Chae, Dongho ;

Degond, Pierre ;

Liu, Jian-Guo .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (03) :555-565

[7] the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics [J].

Chae, Dongho ;

Lee, Jihoon .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (11) :3835-3858

[8] On the temporal decay for the Hall-magnetohydrodynamic equations [J].

Chae, Dongho ;

Schonbek, Maria .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (11) :3971-3982

[9] Local theory in critical spaces for compressible viscous and heat-conductive gases [J].

Danchin, R .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (7-8) :1183-1233

[10] On the Weak Solutions to the Maxwell-Landau-Lifshitz Equations and to the Hall-Magneto-Hydrodynamic Equations [J].

Dumas, Eric ;

Sueur, Franck .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 330 (03) :1179-1225

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