Back to Search Start Over

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

Authors :
Li, Zijin
Yang, Meixian
Source :
Acta Applicandae Mathematicae. Oct2022, Vol. 181 Issue 1, p1-17. 17p.
Publication Year :
2022

Abstract

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 θ 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 θ r satisfies a partial Burgers' equation in this situation. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01678019
Volume :
181
Issue :
1
Database :
Academic Search Index
Journal :
Acta Applicandae Mathematicae
Publication Type :
Academic Journal
Accession number :
158547308
Full Text :
https://doi.org/10.1007/s10440-022-00519-5