Blowup of smooth solutions to the  full compressible MHD system with compact density

Baoquan Yuan; Xiaokui Zhao

doi:10.3934/krm.2014.7.195

Article Contents

2014, Volume 7, Issue 1: 195-203. Doi: 10.3934/krm.2014.7.195

This issue Previous Article Global existence and decay of solutions to the Fokker-Planck-Boltzmann equation Next Article

Blowup of smooth solutions to the full compressible MHD system with compact density

Baoquan Yuan^1, and
Xiaokui Zhao^2,

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, Henan
2.
School of Mathematics and Information Science, Henan polytechnic University, Jiaozuo 454000, Henan

Received: July 2013

Revised: September 2013

Published: March 2014

Abstract / Introduction Related Papers Cited by

Abstract

This paper studies the blowup of smooth solutions to the full compressible MHD system with zero resistivity on $\mathbb{R}^{d}$, $d\geq 1$. We obtain that the smooth solutions to the MHD system will blow up in finite time, if the initial density is compactly supported.

Keywords:

Mathematics Subject Classification: Primary: 35Q35; Secondary: 35B44, 76W05.

Citation:

Related Papers

Cited by

References

[1]	D.-F. Bian and B.-L. Guo, Blow-up of smooth solutions to the isentropic compressible MHD equations, to appear in Applicable Analysis, 2013.doi: 10.1080/00036811.2013.766324.
[2]	Y. Cho and B. J. Jin, Blow-up of viscous heat-conducting compressible flows, J. Math. Anal. Appl., 320 (2006), 819-826.doi: 10.1016/j.jmaa.2005.08.005.
[3]	D. Du, J. Li and K. Zhang, Blow-up of smooth solutions to the Navier-Stokes equations for compressible isothermal fluids, Commun. Math. Sci., 11 (2013), 541-546.doi: 10.4310/CMS.2013.v11.n2.a11.
[4]	O. Rozanova, Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy, in Hyperbolic Problems: Theory, Numerics and Applications (eds. E. Tadmor, J.-G. Liu and A. E. Tzavaras), Proc. Sympos. Appl. Math., 67, Part 2, Amer. Math. Soc., Providence, RI, 2009, 911-917.doi: 10.1090/psapm/067.2/2605286.
[5]	O. Rozanova, Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations, J. Differential Equations, 245 (2008), 1762-1774.doi: 10.1016/j.jde.2008.07.007.
[6]	Z. Xin, Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density, Comm. Pure Appl. Math., 51 (1998), 229-240.
[7]	Z. Xin and W. Yan, On blowup of classical solutions to the compressible Navier-Stokes equations, Commun. Math. Sci., 321 (2013), 529-541.doi: 10.1007/s00220-012-1610-0.