带真空无磁扩散不可压磁流体方程柯西问题的局部适定性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 100-125.

带真空无磁扩散不可压磁流体方程柯西问题的局部适定性

陈明涛¹,苏文火^2,*(),臧爱彬²

¹ 山东大学(威海)数学与统计学院山东威海 264209
² 宜春学院应用数学研究中心江西宜春 336000

收稿日期:2019-12-12 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 苏文火 E-mail:suwenhuo@jxycu.edu.cn
基金资助:
国家自然科学基金(11801495);国家自然科学基金(11771382);江西省教育厅科技项目(GJJ201629);山东省自然科学基金(ZR2019MA050)

Local well-Posedness for the Cauchy Problem of 2D Nonhomogeneous Incompressible and Non-Resistive MHD Equations with Vacuum

Mingtao Chen¹,Wenhuo Su^2,*(),Aibin Zang²

¹ School of Mathematics and Statistics, Shandong University, Shandong Weihai 264209
² Center of Applied Mathematics, Yichun University, Jiangxi Yichun 336000

Received:2019-12-12 Online:2021-02-26 Published:2021-01-29
Contact: Wenhuo Su E-mail:suwenhuo@jxycu.edu.cn
Supported by:
the NSFC(11801495);the NSFC(11771382);the Science and Technology Project of Education Department in Jiangxi Province(GJJ201629);the NSF of Shandong Province(ZR2019MA050)

摘要/Abstract

摘要：

该文讨论了在真空远场的密度条件下，二维不可压零磁耗散磁流体力学方程组柯西问题的局部适定性.在初始密度和磁场具有一定的衰减性时，证明了磁流体方程具有唯一的局部强解.当初值满足兼容性条件和适当的正则性条件时，该强解就是经典解.除此之外，文中还给出了一个仅与磁场有关的爆破准则.

关键词: 2D无磁扩散MHD方程, 真空, 经典解, 爆破准则

Abstract:

In this paper, we investigate the Cauchy problem of the nonhomogeneous incompressible and non-resistive MHD on ${\Bbb R}$² with vacuum as far field density and prove that the 2D Cauchy problem has a unique local strong solution provided that the initial density and magnetic field decay not too slow at infinity. Furthermore, if the initial data satisfy some additional regularity and compatibility conditions, the strong solution becomes a classical one. Moreover, we also establish a blowup criterion which depends only on the Magnetic fields.

Key words: 2D non-resistive MHD equations, Vacuum, Classical solutions, Blowup criterion

中图分类号:

O175.2

陈明涛,苏文火,臧爱彬. 带真空无磁扩散不可压磁流体方程柯西问题的局部适定性[J]. 数学物理学报, 2021, 41(1): 100-125.

Mingtao Chen,Wenhuo Su,Aibin Zang. Local well-Posedness for the Cauchy Problem of 2D Nonhomogeneous Incompressible and Non-Resistive MHD Equations with Vacuum[J]. Acta mathematica scientia,Series A, 2021, 41(1): 100-125.

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