On a Single-Component Regularity Criterion for the Non-resistive Axially Symmetric Hall-MHD System

被引：0
|
作者：
Li, Zijin [1 ,2 ]
Yang, Meixian [1 ]
机构：
[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China
[2] Nanjing Xinda Inst Safety & Emergency Management, Nanjing 210044, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2022年 / 181卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Incompressible; Non-resistive; Hall-MHD system; Axially symmetric; Regularity criterion; One component; GLOBAL EXISTENCE; WELL-POSEDNESS; DECAY; MAGNETOHYDRODYNAMICS; EQUATIONS; STABILITY; EULER;
D O I：
10.1007/s10440-022-00519-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A one-component regularity criterion for the non-resistive axially symmetric Hall-MHD system is given in this paper. More precisely, we show that strong solutions to a family of axially symmetric initial data, whose velocity and current density have trivial swirl components, could be smoothly extended beyond a possible blow-up time T-* if and only if the swirl component of the magnetic field h(theta) satisfies a Beale-Kato-Majda-type criterion. See (1.5) below. This criterion is not trivial even if the velocity field vanishes since the quantity h(theta)/r satisfies a partial Burgers' equation in this situation.
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页数：17
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