A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density

Anthony Suen

doi:10.3934/dcds.2013.33.3791

Article Contents

2013, Volume 33, Issue 8: 3791-3805. Doi: 10.3934/dcds.2013.33.3791

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A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density

Anthony Suen^1,

1.
Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419

Received: May 31, 2012

Revised: September 30, 2012

Published: July 2013

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Abstract

We study an initial boundary value problem for the 3D magnetohydrodynamics (MHD) equations of compressible fluids in $\mathbb{R}^3$. We establish a blow-up criterion for the local strong solutions in terms of the density and magnetic field. Namely, if the density is away from vacuum ($\rho= 0$) and the concentration of mass ($\rho=\infty$) and if the magnetic field is bounded above in terms of $L^\infty$-norm, then a local strong solution can be continued globally in time.

Keywords:

Blow-up criteria,
compressible magnetohydrodynamics.

Mathematics Subject Classification: 76W05, 35Q35.

Citation:

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