On regularity criteria for MHD system in anisotropic Lebesgue spaces

Kun Cheng; Yong Zeng; Kun Cheng; Yong Zeng

doi:10.3934/era.2023239

Electronic Research Archive

2023, Volume 31, Issue 8: 4669-4682. doi: 10.3934/era.2023239

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Research article

On regularity criteria for MHD system in anisotropic Lebesgue spaces

Kun Cheng ,
Yong Zeng ^,

School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received: 29 March 2023 Revised: 14 June 2023 Accepted: 24 June 2023 Published: 30 June 2023

This paper concerns the regularity criteria of the three-dimensional magnetohydrodynamic (MHD) system in anisotropic Lebesgue spaces. Two regularity results were proved under additional assumptions on the horizontal components of the velocity field $ {{\bf{u}}} $ and the magnetic field $ {{\bf{B}}} $, or directions of Elsässer's variables $ {{\bf{u}}}\pm{{\bf{B}}} $.
- MHD system,
- regularity criteria,
- anisotropic Lebesgue space,
- sum spaces,
- Elsässer's variables
Citation: Kun Cheng, Yong Zeng. On regularity criteria for MHD system in anisotropic Lebesgue spaces[J]. Electronic Research Archive, 2023, 31(8): 4669-4682. doi: 10.3934/era.2023239

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Abstract

This paper concerns the regularity criteria of the three-dimensional magnetohydrodynamic (MHD) system in anisotropic Lebesgue spaces. Two regularity results were proved under additional assumptions on the horizontal components of the velocity field $ {{\bf{u}}} $ and the magnetic field $ {{\bf{B}}} $, or directions of Elsässer's variables $ {{\bf{u}}}\pm{{\bf{B}}} $.

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