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In this paper, we prove a blow-up criterion in terms of the magnetic field H and the mass density $$\rho $$ ρ for the strong solutions to the initial boundary value problem of the 3D isentropic compressible MHD equations with zero magnetic diffusion and initial vacuum. More precisely, we show that the upper bounds of $$(H,\rho )$$ ( H , ρ ) control the possible blow-up (see Rozanova in Proceedings of symposia in applied mathematics, 2009 ; Xin in Commun Pure Appl Math 51:0229–0240, 1998 ; Yuan and Zhao in Kinet Relat Models 7:195–203, 2014 ) for strong solutions.

Blow-Up Criterion for the 3D Non-resistive Compressible Magnetohydrodynamic Equations