On some new global existence results for 3D magnetohydrodynamic equations

被引：26

作者：

He, Cheng ^{[1
]}

Huang, Xiangdi ^{[2
,3
]}

Wang, Yun ^{[4
]}

机构：

[1] Natl Nat Sci Fdn China, Dept Math & Phys Sci, Div Math, Beijing 100085, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China

[3] Osaka Univ, Dept Pure & Appl Math, Grad Sch Informat Sci & Technol, Osaka, Japan

[4] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China

来源：

NONLINEARITY | 2014年 / 27卷 / 02期

关键词：

magnetohydrodynamics equations; global strong solution; cancellation; WEAK SOLUTIONS; MHD EQUATIONS; REGULARITY CRITERIA; TURBULENCE; DYNAMICS;

D O I：

10.1088/0951-7715/27/2/343

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the incompressible magnetohydrodynamic equations in R-3. We prove that if the difference between the magnetic field and the velocity is small initially then it will remain forever, thus resulting in a global strong solution without the smallness restriction on the size of initial velocity or magnetic field. In other words, magnetic field can indeed regularize Navier-Stokes equations, due to cancellation.

引用

页码：343 / 352

页数：10

共 19 条

[1] LONGTIME DYNAMICS OF A CONDUCTIVE FLUID IN THE PRESENCE OF A STRONG MAGNETIC-FIELD [J].

BARDOS, C ;

SULEM, C ;

SULEM, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 305 (01) :175-191

[2] Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD [J].

Caflisch, RE ;

Klapper, I ;

Steele, G .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 184 (02) :443-455

[3]

Duvaut G., 1972, Arch. Ration. Mech. Anal, V46, P241, DOI DOI 10.1007/BF00250512

[4] SELF-ORGANIZATION PROCESSES IN CONTINUOUS MEDIA [J].

HASEGAWA, A .

ADVANCES IN PHYSICS, 1985, 34 (01) :1-42

[5] On the regularity of weak solutions to the magnetohydrodynamic equations [J].

He, C ;

Xin, ZP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 213 (02) :235-254

[6] Remark on the regularity for weak solutions to the magnetohydrodynamic equations [J].

He, Cheng ;

Wang, Yun .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2008, 31 (14) :1667-1684

[7] On the regularity criteria for weak solutions to the magnetohydrodynamic equations [J].

He, Cheng ;

Wang, Yun .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 238 (01) :1-17

[8] Regularity criteria of the magnetohydrodynamic equations in bounded domains or a half space [J].

Kang, Kyungkeun ;

Kim, Jae-Myoung .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (02) :764-794

[9]

Liu H X, 2013, NONLINEARITY, V26, P219

[10] Well-posedness for the incompressible magneto-hydrodynamic system [J].

Miao, Changxing ;

Yuan, Baoquan ;

Zhang, Bo .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2007, 30 (08) :961-976

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