In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy (∥ρ∥L∞(0,T;L∞)+∥u∥C([0,T];L3)<∞), then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over [0,T]. Notably, our analysis accommodates the presence of an initial vacuum.
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Wang et al. (2024) studied this question.
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