Abstract
In this paper, we investigate the singularity formulation and blow-up mechanism to the compressible magnetohydrodynamic (MHD) flows in two dimensions. It is essentially shown that the mass of the compressible MHD fluid will concentrate in some spatial points, even if the initial density contains vacuum states, provided that the strong or smooth solution develops singularity in finite time. The result indicates that there is no possibility of formulating the other kinds of singularities, such as the vanishing of vacuum states, the appearance of vacuum states in the non-vacuum region or even milder ones, before the density concentrates at some point. It also implies the global regularity of the strong solution to the compressible MHD system, provided that the density remains bounded.
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