可压缩磁流体方程光滑解的爆破性

Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (4): 715-721.

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Blow-Up of Smooth Solutions to the Compressible MHD Equations

Bian Dongfen¹, Tang Tong²

1. School of mathematics and statistics, Beijing Institute of Technology, Beijing 100081;
2. Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098

Received:2015-10-24 Revised:2016-04-12 Online:2016-08-26 Published:2016-08-26
Supported by:
Supported by the NSFC(11501028,11471323,11526073,11271192),the Natural Science Foundation of Jiangsu Province(BK20150794) and China Postdoctoral Foundation Funded Project(2015M570939)

Abstract

CLC Number:

O175.2

Bian Dongfen, Tang Tong. Blow-Up of Smooth Solutions to the Compressible MHD Equations[J].Acta mathematica scientia,Series A, 2016, 36(4): 715-721.

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[1] Bian D F, Guo B L. Blow-up of smooth solutions to the isenropic compressibel MHD equations. Appl Anal, 2014, 93: 190-197
[2] Du D P, Li J Y, Zhang K J. Blow-up of smooth solution to the Navier-Stokes equations for compressible isothermal fluids. Commun Math Sci, 2011, 11: 541-546
[3] Du L L, Wang Y F. Blowup criterion for 3-dimensional compressible Navier-Stokes equations involving velocity divergence. Commun Math Sci, 2014, 12: 1427-1435
[4] Fan J S, Yu W H. Strong solution to the compressible magnetohydrodynamic equations with vacuum. Nonlinear Anal, 2009, 10: 392-409
[5] Fang D Y, Zhang T. The Naiver-Stokes Equations with Variable Viscous. Zhejiang: Zhejiang University Press, 2008
[6] Huang X D, Li J. Serrin-type blowup criterion for viscous, compressible, and heat conducting Navier-Stokes and magnetohydrodynamic flows. Comm Math Phys, 2013, 324: 147-171
[7] Rozanova O. Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy. Hyperbolic Problems: Theory, Numerics and Applications, 2008, 67: 911-917
[8] Sideris T C. Formation of singularities in three-dimensional compressible fluids. Comm Math Phys, 1985, 101: 475-485
[9] Wang Y F, Li S. Global regularity for the Cauchy problem of three-dimensional compressible magnetohydrodynamics equations. Nonlinear Anal Real World Appl, 2014, 18: 23-33
[10] Xin Z P. Blow-up of smooth solution to the compressible Naiver-Stokes equations with compact density. Comm Pure Appl Math, 1998, 51: 229-240
[11] Xin Z P, Yan W. On blow-up of classical solutions to the compressible Naiver-Stokes equations. Comm Math Phys, 2013, 321: 529-541
[12] Xu X Y, Zhang J W. A blow-up criterion for 3D compressible magnetohydrodynamic equations with vacuum. Math Models Methods Appl Sci, 2012, 22: 1150010
[13] Yuan B Q. On the blow-up criterion of smooth solutions to the MHD system in BMO space. Acta Math Appl Sin (Engl Ser), 2006, 22: 413-418
[14] Yuan B Q, Zhao X K. Blowup of smooth solutions to the full compressible MHD system with compact density. Kinet Relat Models, 2014, 7: 195-203
[15] Zhang J J, Guo B L. Global existence of solution for thermally radiative magnetohydrodynamic equations with the displacement current. J Math Phys, 2013, 54: 013519

Blow-Up of Smooth Solutions to the Compressible MHD Equations

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