In this paper, we prove a blow-up criterion in terms of the magnetic field H and the mass density \(\rho \) 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 \((H,\rho )\) 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.

中文翻译：

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3D非电阻可压缩磁流体动力学方程的爆破判据

在本文中，我们用磁场H和质量密度\（\ rho \）证明了零磁扩散和零磁场下3D等熵可压缩MHD方程初始边值问题的强解的爆破准则。初始真空。更确切地说，我们证明\（（H，\ rho）\）的上限控制了可能的爆发（请参阅Rozanova，应用数学研讨会论文集，2009年； Xin，Commun Pure Appl Math 51：0229-0240 （1998年；袁和赵在Kinet Relat Models 7：195–203，2014年）中找到了有效的解决方案。