三维有界区域上可压缩霍尔磁流体动力系统  

Compressible Hall magnetohydrodynamic systems in three-dimensional bounded regions

作　　者：叶秋慧 郭闪闪 YE Qiuhui;GUO Shanshan(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《内江师范学院学报》2025年第4期34-42,共9页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(12001074);重庆市教委科学技术研究项目(KJQN202000536);重庆市科学技术局科学研究项目(cstc2020jcyj-msxmX0606)。

摘　　要：为了使磁流体动力系统强解的全局存在性和渐近性态更具一般性,更好地刻画在三维空间里该系统的性质.本文利用能量估计的方法,得到系统强解的全局性存在性和渐近性.首先给出该系统的局部存在性,再给出区域内部和边界附近的先验估计,基于区域内部和边界附近的精细能量估计,利用截断函数和有限覆盖方法,对边界区域进行拉平,最后结合局部存在性,用三个步骤对提出的定理进行证明.由此,得到了有界域内强解的全局存在性、唯一性及指数收敛速度估计.针对三维可压缩霍尔磁流体动力系统,证明了此系统在边界光滑的有界区域内的全局存在性和渐近性,解决了不能用经典的能量方法估计边界处的空间导数等问题.In order to make the global existence and asymptotic properties of the strong solution of the magnetohydrodynamic system more general,and better describe the properties of the system in three-dimensional space.It is mainly by using the method of energy estimation to obtain the global existence and asymptotic nature of the strong solution of the system.Firstly,the local existence of the system is given,and then the prior estimation of the system within the region and near the boundary is given,basing on the fine energy estimation within the region and near the boundary,the truncation function and the finite coverage method are used to level the boundary region,and finally the proposed theorem is proved in three steps by combining the local existence.Basing on this,the global existence,uniqueness and exponential convergence speed estimation of the strong solution in the bounded domain are obtained.For the three-dimensional compressible Hall magnetohydrodynamic system,the global existence and asymptotic properties of the system in the bounded region with smooth boundaries are proved,and the problem that the spatial derivative at the boundary cannot be estimated by the classical energy method is solved.

关 键 词：可压缩 霍尔磁流体动力系统(Hall-MHD) 全局存在性 渐近性 

分 类 号：O175.29[理学—数学]