# American Institute of Mathematical Sciences

August  2013, 33(8): 3791-3805. doi: 10.3934/dcds.2013.33.3791

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

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

Received  June 2012 Revised  October 2012 Published  January 2013

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.
Citation: Anthony Suen. A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3791-3805. doi: 10.3934/dcds.2013.33.3791
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