三维稳态 MHD 方程和 Hall-MHD 方程的 Liouville 型定理
三维稳态 MHD 方程和 Hall-MHD 方程的 Liouville 型定理
复制标题
DOI：
10.1360/ssm-2022-0059
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Zhengan Yao
中科院分区：
文献类型：
--
作者：
Yanping Zhou;Qunyi Bie;Qiru Wang;Zhengan Yao
本文研究了三维定常磁流体动力学方程和Hall-MHD方程的Liouville型定理。在局部Morrey空间的框架下，我们克服了压力项对无穷能量解的估计，得到了保证这两类系统存在唯一平凡解的充分条件.然后，利用Lorentz空间与局部Morrey空间的嵌入关系，给出了Lorentz空间中两类系统的Liouville型定理。所得结果不需要有限Dirichlet积分的条件，推广和改进了Lebesgue空间框架下关于这两类系统的已有结果。
In this paper, we study the Liouville type theorems of the MHD (magnetohydrodynamics) equation and Hall-MHD equation in three-dimensional steady states. In the framework of local Morrey space, we overcome the estimations of the pressure term with an infinite energy solution and obtain some sufficient conditions to guarantee the existence of a unique trivial solution for these two kinds of systems. Then, by using the embedding relations between the Lorentz spaces and local Morrey spaces, we give the Liouville type theorems for the two kinds of systems in the Lorentz spaces. The obtained results do not need the condition of finite Dirichlet integral, and hence generalize and improve some existing results about the two kinds of systems in the framework of Lebesgue space.