论文标题
3D可压缩热传导磁性水力学方程的熵结合的溶液，无穷大。
Entropy-bounded solutions to the 3D compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity
论文作者
论文摘要
对粘性，可压缩和热传导真空区域的磁性流动流的熵行为的数学分析是一个具有挑战性的问题，因为熵的管理方程在真空区是高度退化和奇异的。特别是，未知熵是否保持其界限。在本文中，我们研究了库奇问题的三维（3D）可压缩的热传导磁性水动力方程，仅在无穷大时真空吸尘器。我们表明，只要初始密度在无穷大时，熵和温度的$ l^2 $规律都可以传播，熵的统一界限和$ l^2 $的规律性可以传播。主要工具基于Li and Xin（Arxiv：2111.14057）开发的奇异加权能量估计和DE Giorgi型迭代技术，适用于3D完整可压缩的Navier-Stokes系统。开发了一些新的数学技术和有用的估计值，以推断熵上的下限和上限。
The mathematical analysis on the behavior of the entropy for viscous, compressible, and heat conducting magnetohydrodynamic flows near the vacuum region is a challenging problem as the governing equation for entropy is highly degenerate and singular in the vacuum region. In particular, it is unknown whether the entropy remains its boundedness. In the present paper, we investigate the Cauchy problem to the three-dimensional (3D) compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity only. We show that the uniform boundedness of the entropy and the $L^2$ regularities of the velocity and temperature can be propagated provided that the initial density decays suitably slow at infinity. The main tools are based on singularly weighted energy estimates and De Giorgi type iteration techniques developed by Li and Xin (arXiv:2111.14057) for the 3D full compressible Navier-Stokes system. Some new mathematical techniques and useful estimates are developed to deduce the lower and upper bounds on the entropy.
