部分耗散的三维不可压Hall-MHD方程组的整体正则性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1754-1767.

部分耗散的三维不可压Hall-MHD方程组的整体正则性

杜保营*(),刘金兴

^{宜宾学院理学部, 四川宜宾 644000}

收稿日期:2021-08-16 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 杜保营 E-mail:Dubaoying99@163.com
基金资助:
宜宾学院高层次人才启航项目(2021QH07)

Global Regularity for the Incompressible 3D Hall-Magnetohydrodynamics with Partial Dissipation

Baoying Du*(),Jinxing Liu

^{Faculty of Science, Yibin University, Sichuan Yibin 644000}

Received:2021-08-16 Online:2022-12-26 Published:2022-12-16
Contact: Baoying Du E-mail:Dubaoying99@163.com
Supported by:
the High-level Talent Sailing Project of Yibin University(2021QH07)

摘要/Abstract

摘要：

该文研究了具有部分耗散的三维不可压霍尔-磁流体力学方程组, 在Sobolev范数意义下, 运用能量估计的一些特殊性质, 得到了大初值经典解的局部存在性.另外, 当初值在适当Sobolev范数意义下充分小时, 该文也得到了经典解的整体存在性.

关键词: 整体正则性, 霍尔-磁流体方程组, 部分耗散, 经典解, 局部存在性

Abstract:

In this paper, we study the incompressible 3D Hall-magnetohydrodynamic equations with partial dissipation, by the special property of the energy estimate in term of Sobolev norm, we obtain the local existence of classical solutions for large initial data. We also prove the global existence of the classical solutions, the smallness conditions of which are given by the suitable Sobolev norms.

Key words: Global regularity, Hall-magnetohydrodynamics, Partial dissipation, Classical solutions, Local existence

中图分类号:

O175.29

杜保营,刘金兴. 部分耗散的三维不可压Hall-MHD方程组的整体正则性[J]. 数学物理学报, 2022, 42(6): 1754-1767.

Baoying Du,Jinxing Liu. Global Regularity for the Incompressible 3D Hall-Magnetohydrodynamics with Partial Dissipation[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1754-1767.

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