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 $3$Dcompressible isentropic MHD equations with zero magnetic diffusion and initialvacuum. More precisely, we show that the $L^\infty$ norms of $(H,\rho)$ controlthe possible blow-up (see \cite{olga}\cite{zx}) for strong solutions, whichmeans that if a solution of the compressible isentropic non-resistive MHDequations is initially smooth and loses its regularity at some later time, thenthe formation of singularity must be caused by losing the bound of the$L^\infty$ norm of $H$ or $\rho$ as the critical time approaches.
展开▼
机译：在本文中，我们证明了磁场为$ H $且质量密度为$ \ rho $的爆破准则，用于求解零磁扩散和初始真空的$ 3 $ D可压缩等熵MHD方程的强解。更确切地说，我们证明了$（H，\ rho）$的$ L ^ \ infty $范数控制了强解决方案可能发生的爆炸（请参见\ cite {olga} \ cite {zx}），这意味着如果有解决方案，可压缩的等熵非电阻MHD方程最初是平滑的，并在以后的某个时间失去规律性，那么奇异性的形成必须是由于失去了$ H ^或$ \ rho $的$ L ^ \ infty $范数的界关键时间临近。
展开▼
