三维稳态MHD方程和Hall-MHD方程的Liouville型定理  

On Liouville type theorems for three-dimensional stationary MHD and Hall-MHD equations

作　　者：周艳平[1,2] 别群益 王其如 姚正安[3] Yanping Zhou;Qunyi Bie;Qiru Wang;Zheng-An Yao

机构地区：[1]三峡大学三峡数学研究中心,宜昌443002 [2]三峡大学理学院,宜昌443002 [3]中山大学数学学院,广州510275

出　　处：《中国科学：数学》2023年第3期431-440,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11901346,11871305,11971496和12071491)资助项目。

摘　　要：本文研究三维稳态情形下的磁流体动力学(magnetohydrodynamics,MHD)方程和具Hall效应的磁流体动力学(Hall-MHD)方程的Liouville型定理.在局部Morrey空间框架下,本文克服具有无限能量解的压力项的估计问题,得到若干充分条件以保证这两类方程存在唯一的平凡解.然后,利用Lorentz空间和局部Morrey空间的嵌入关系,给出这两类方程在Lorentz空间中的Liouville型定理.所得结果不需要有限Dirichlet积分条件,从而推广和改进了已有的关于这两类方程在Lebesgue空间框架下的一些结果.In this paper,we study the Liouville type theorems of the MHD(magnetohydrodynamics)equations and Hall-MHD equations in three-dimensional steady states.In the framework of local Morrey spaces,we overcome the estimations of the pressure term with an infinite energy solution and obtain some sufcient 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 we generalize and improve some existing results about the two kinds of systems in the framework of Lebesgue spaces.

关 键 词：稳态MHD方程 稳态Hall-MHD方程 LIOUVILLE型定理 局部Morrey空间 LORENTZ空间 

分 类 号：O175[理学—数学]