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Remarks on the regularity criteria for the axisymmetric MHD system

Volume 126 / 2021

Zujin Zhang, Yali Zhang Annales Polonici Mathematici 126 (2021), 79-95 MSC: Primary 35Q35; Secondary 35B65, 76D03. DOI: 10.4064/ap200221-15-9 Published online: 11 December 2020

Abstract

We show several weighted regularity criteria for the axisymmetric solutions to the three-dimensional magnetohydrodynamic equations, involving $u^r, u^z$; $u^r, b^r, \partial _ru^z, \partial _rb^z$; $u^r,b^r, \partial _zu^\theta , \partial _zb^\theta $; $u^r, b^r, \partial _ru^\theta , \partial _rb^\theta $; or $\omega ^\theta $, where $u^r,u^\theta ,u^z$ are the angular, swirl and axial components of the velocity respectively and $\omega ^\theta $ denotes the swirl component of the vorticity.

Authors

  • Zujin ZhangSchool of Mathematics and Computer Science
    Gannan Normal University
    Ganzhou 341000, Jiangxi, P.R. China
    e-mail
  • Yali ZhangSchool of Mathematics and Computer Science
    Gannan Normal University
    Ganzhou 341000, Jiangxi, P.R. China
    e-mail

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