Global weighted regularity for the 3D axisymmetric non-resistive MHD system

Wenjuan Liu; Zhouyu Li; Wenjuan Liu; Zhouyu Li

doi:10.3934/math.20241017

AIMS Mathematics

2024, Volume 9, Issue 8: 20905-20918. doi: 10.3934/math.20241017

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Research article

Global weighted regularity for the 3D axisymmetric non-resistive MHD system

Wenjuan Liu ¹,
Zhouyu Li ^{2
,
,}

1.
School of Mathematics, Northwest University, Xi'an 710069, China
2.
School of Sciences, Xi'an University of Technology, Xi'an 710054, China

Received: 19 April 2024 Revised: 24 June 2024 Accepted: 25 June 2024 Published: 28 June 2024
MSC : 35B65, 35Q35, 76D03

We consider the regularity criteria of axisymmetric solutions to the non-resistive MHD system with non-zero swirl in $ \mathbb{R}^{3} $. By applying a new anisotropic Hardy-Sobolev inequality in mixed Lorentz spaces, we show that strong solutions to this system can be smoothly extended beyond the possible blow-up time $ T $ if the horizontal angular component of the velocity belongs to anisotropic Lorentz spaces.
- non-resistive MHD system,
- anisotropic Lorentz spaces,
- regularity criteria
Citation: Wenjuan Liu, Zhouyu Li. Global weighted regularity for the 3D axisymmetric non-resistive MHD system[J]. AIMS Mathematics, 2024, 9(8): 20905-20918. doi: 10.3934/math.20241017

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Abstract

We consider the regularity criteria of axisymmetric solutions to the non-resistive MHD system with non-zero swirl in $ \mathbb{R}^{3} $. By applying a new anisotropic Hardy-Sobolev inequality in mixed Lorentz spaces, we show that strong solutions to this system can be smoothly extended beyond the possible blow-up time $ T $ if the horizontal angular component of the velocity belongs to anisotropic Lorentz spaces.

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