On the splash singularity for the free-boundary problem of the viscous and non-resistive incompressible magnetohydrodynamic equations in 3D

IF 2.4 2区 数学 Q1 MATHEMATICS
Guangyi Hong , Tao Luo , Zhonghao Zhao
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引用次数: 0

Abstract

In this paper, the existence of finite-time splash singularity is proved for the free-boundary problem of the viscous and non-resistive incompressible magnetohydrodynamic (MHD) equations in R3, based on a construction of a sequence of initial data alongside delicate estimates of the solutions. The result and analysis in this paper generalize those by Coutand and Shkoller in [14, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 2019] from the viscous surface waves to the viscous conducting fluids with magnetic effects for which non-trivial magnetic fields may present on the free boundary. The arguments in this paper also hold for any space dimension d2.
关于三维粘性和非阻力不可压缩磁流体动力学方程自由边界问题的飞溅奇点
本文基于初始数据序列的构造以及解的微妙估计,证明了 R3 中粘性和非阻性不可压缩磁流体动力学(MHD)方程的自由边界问题存在有限时间飞溅奇点。本文的结果和分析概括了 Coutand 和 Shkoller 在[14, Ann. Inst. H. Poincaré C Anal. Non Linéaire,2019]中从粘性表面波到具有磁效应的粘性导电流体的结果和分析,其中自由边界上可能存在非三维磁场。本文的论点在空间维数 d≥2 时也同样成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.40
自引率
8.30%
发文量
543
审稿时长
9 months
期刊介绍: The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics
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