三维 Hall-magnetohydrodynamic 方程的整体小解

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 586-594.

三维 Hall-magnetohydrodynamic 方程的整体小解

于洋海^1,^*(),王慧¹(),吴星²()

1.安徽师范大学数学与统计学院安徽芜湖 241002
2.河南农业大学信息与管理科学学院郑州 450002

收稿日期:2022-09-27 修回日期:2023-05-16 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *于洋海, Email: yuyanghai214@sina.com
作者简介:王慧, Email: 1817688537@qq.com;|吴星, Email: ny2008wx@163.com
基金资助:
国家自然科学基金(12101011)

Global Small Solutions of 3D Hall-Magnetohydrodynamic Equations

Yu Yanghai^1,^*(),Wang Hui¹(),Wu Xing²()

1. School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241002
2. College of Information and Management Science, Henan Agricultural University, Zhengzhou 450002

Received:2022-09-27 Revised:2023-05-16 Online:2024-06-26 Published:2024-05-17
Supported by:
NSFC(12101011)

摘要/Abstract

摘要：

该文研究 $\mathbb{R}^3$ 上的不可压缩的带霍尔效应的磁流体力学方程的 Cauchy 问题. 假设初始速度的水平分量或水平分量的和及初始磁场的 $\dot{B}_{2,1}^{>12}$ 范数充分小, 该文证明了该方程存在整体光滑解, 改进了 Chae 和 Lee (J. Differ. Equ. 2014) 的结果.

关键词: Hall-magnetohydrodynamic 方程, 整体小解

Abstract:

In this paper, we establish the global solutions to the three-dimensional incompressible Hall-MHD equations provided that the initial horizontal velocity is sufficiently small, which improves the result given by Chae and Lee (J. Differ. Equ. 2014).

Key words: Hall-magnetohydrodynamic Equations, Global small solutions

中图分类号:

O175.2

于洋海, 王慧, 吴星. 三维 Hall-magnetohydrodynamic 方程的整体小解[J]. 数学物理学报, 2024, 44(3): 586-594.

Yu Yanghai, Wang Hui, Wu Xing. Global Small Solutions of 3D Hall-Magnetohydrodynamic Equations[J]. Acta mathematica scientia,Series A, 2024, 44(3): 586-594.

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