Strong solution to the compressible magnetohydrodynamic equations with vacuum

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Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows (2012, background): “1) with large initial data were respectively obtained by [38] and [7] in the cases that the initial density is strictly positive and that the density is allowed to vanish initially, whether the unique local strong solution can exist globally is an outstanding challenging open problem.”