On formation of singularity of the full compressible magnetohydrodynamic equations with zero heat conduction
On formation of singularity of the full compressible magnetohydrodynamic equations with zero heat conduction
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DOI：
10.1512/iumj.2019.68.7749
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发表时间：
2017-05
影响因子：
1.1
通讯作者：
X. Zhong
中科院分区：
文献类型：
--
作者：
X. Zhong
研究了具有零热传导的三维完全可压缩磁流体动力学方程组Cauchy问题的奇性形成和强解的破裂。证明了当初始密度为真空时，当变形张量D（u）和压力P满足$L^{1}（0，T;L^\infty）}+ P L^{\infty}（0，T; L ^\infty）}<\infty$时，强解整体存在.特别是，该标准是独立的磁场。Lam{\'e}系统的近似估计和一些精细的能量估计在证明中起着至关重要的作用。
We are concerned with the formation of singularity and breakdown of strong solutions to the Cauchy problem of the three-dimensional full compressible magnetohydrodynamic equations with zero heat conduction. It is proved that for the initial density allowing vacuum, the strong solution exists globally if the deformation tensor $\mathfrak{D}(\mathbf{u})$ and the pressure $P$ satisfy $\|\mathfrak{D}(\mathbf{u})\|_{L^{1}(0,T;L^\infty)}+\|P\|_{L^{\infty}(0,T;L^\infty)}<\infty$. In particular, the criterion is independent of the magnetic field. The logarithm-type estimate for the Lam{\'e} system and some delicate energy estimates play a crucial role in the proof.