THE ENERGY CONSERVATIONS AND LOWER BOUNDS FOR POSSIBLE SINGULAR SOLUTIONS TO THE 3D INCOMPRESSIBLE MHD EQUATIONS

被引:0
作者
Jae-Myoung KIM
机构
[1] DepartmentofMathematicsEducationAndongNationalUniversity
关键词
MHD equation; lower bounds; incompressible;
D O I
暂无
中图分类号
O175 [微分方程、积分方程];
学科分类号
070104 ;
摘要
In this note, we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations. Moreover, we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.
引用
收藏
页码:237 / 244
页数:8
相关论文
共 10 条
[1]  
Two regularity criteria for the 3D MHD equations[J] . Chongsheng Cao,Jiahong Wu. Journal of Differential Equations . 2009 (9)
[2]   Partial regularity of solutions to the magnetohydrodynamic equations [J].
Vyalov V. .
Journal of Mathematical Sciences, 2008, 150 (1) :1771-1786
[3]   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
[4]  
Non-Uniform Decay of MHD Equations With and Without Magnetic Diffusion[J] . Ruben Agapito,Maria Schonbek. Communications in Partial Differential Equations . 2007 (11)
[5]   Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations [J].
He, C ;
Xin, ZP .
JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 227 (01) :113-152
[6]  
On the regularity of weak solutions to the magnetohydrodynamic equations[J] . Cheng He,Zhouping Xin. Journal of Differential Equations . 2004 (2)
[7]   Well-posedness for the dumbbell model of polymeric fluids [J].
Weinan, E ;
Li, TJ ;
Zhang, PW .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 248 (02) :409-427
[8]  
Large-time behaviour of solutions to the magneto-hydrodynamics equations[J] . M. E. Schonbek,T. P. Schonbek,Endre Süli. Mathematische Annalen . 1996 (1)
[9]  
Inéquations en thermoélasticité et magnétohydrodynamique[J] . G. Duvaut,J. L. Lions. Archive for Rational Mechanics and Analysis . 1972 (4)
[10]  
Multiplicative Inequalities of Carlson Type and Interpolation .2 Larsson L,Maligranda L,Pecaric J,Persson L-E. World Scientific Publishing Co Pte Ltd . 2006