二维有界域中零电阻率全可压缩磁流体动力学方程奇异性的形成

Pub Date : 2023-11-08 DOI:10.1007/s10255-023-1094-z

Xin Zhong

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引用次数: 0

摘要

我们研究了在有界域中具有零电阻率的二维（2D）完全可压缩磁流体动力学方程的强解的奇异性形成。利用能量方法和对数型临界Sobolev不等式，我们证明了如果变形张量的最大范数的时间积分是有界的，则强解是全局存在的。我们的结果与三维不可压缩Euler方程的Ponce准则相同。特别地，它与磁场和温度无关。此外，允许初始真空状态。

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Formation of Singularity for Full Compressible Magnetohydrodynamic Equations with Zero Resistivity in Two Dimensional Bounded Domains

We are concerned with singularity formation of strong solutions to the two-dimensional (2D) full compressible magnetohydrodynamic equations with zero resistivity in a bounded domain. By energy method and critical Sobolev inequalities of logarithmic type, we show that the strong solution exists globally if the temporal integral of the maximum norm of the deformation tensor is bounded. Our result is the same as Ponce’s criterion for 3D incompressible Euler equations. In particular, it is independent of the magnetic field and temperature. Additionally, the initial vacuum states are allowed.

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