MHD系统和Hall-MHD系统解的局部适定性

doi:10.13438/j.cnki.jdzk.2025.04.002

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (4): 5-10.DOI: 10.13438/j.cnki.jdzk.2025.04.002

MHD系统和Hall-MHD系统解的局部适定性

王苗苗，马德宜，别群益

（三峡大学理学院，湖北宜昌 443002）

出版日期:2025-07-25 发布日期:2025-08-05
作者简介:王苗苗(1998—)，女，河南濮阳人，三峡大学理学院硕士生，主要从事偏微分方程研究
基金资助:
国家自然科学基金资助项目(11871305)

Local Well-Posedness of Solutions to the MHD and Hall-MHD Systems

WANG Miaomiao,MA Deyi,BIE Qunyi

(College of Science,China Three Gorges University,Yichang 443002,Hubei China)

Online:2025-07-25 Published:2025-08-05

摘要/Abstract

摘要：研究了三维广义不可压缩磁流体动力学 (MHD) 系统和Hall磁流体动力学 (Hall-MHD) 系统的解的局部适定性.先给出了Morrey空间中热核的估计，再利用Picard不动点原理证明了在适当的α₁，α₂条件下，当初始值(u₀,b₀)属于齐次Morrey空间M·r,p(R³)时（其中1<r<p<+∞，p>3），这2个系统的解(u,b)在齐次Morrey空间中是局部适定的.

关键词： MHD系统, Hall-MHD系统, 局部适定性, Morrey空间

Abstract: This paper studies the local well-posedness for the 3D generalized incompressible magneto-hydrodynamic (MHD) and Hall-magnetohydrodynamic (Hall-MHD) systems.Firstly,we present the estimations of the heat kernel in Morrey spaces.Then,by using Picard's fixed point argument,we prove that when parameters α₁,α₂ satisfy certain conditions and the initial data satisfies (u₀,b₀)∈Mr,p(R³)，where 1<r<p<+∞ and p>3，the solutions to these two systems are locally well-posed in homogeneous Morrey spaces.

Key words: MHD system, Hall-MHD system, local well-posedness, Morrey spaces

王苗苗, 马德宜, 别群益. MHD系统和Hall-MHD系统解的局部适定性[J]. 吉首大学学报（自然科学版）, 2025, 46(4): 5-10.

WANG Miaomiao, MA Deyi, BIE Qunyi. Local Well-Posedness of Solutions to the MHD and Hall-MHD Systems[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(4): 5-10.

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MHD系统和Hall-MHD系统解的局部适定性

Local Well-Posedness of Solutions to the MHD and Hall-MHD Systems

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