Regularity results of 2D magneto-micropolar equations without kinematic dissipation

Menghan Gong; Weixian Sun; Wenjuan Wang

doi:10.3934/dcdsb.2024003

Article Contents

2024, Volume 29, Issue 8: 3256-3275. Doi: 10.3934/dcdsb.2024003

This issue Previous Article Dynamics of a competition system with lethal boundary conditions in advective environments Next Article Stress formulation and duality approach in periodic homogenization

Regularity results of 2D magneto-micropolar equations without kinematic dissipation

1.
Department of Mathematics and Statistics, Jiangsu Normal University, 101 Shanghai Road, Xuzhou 221116, Jiangsu, China
2.
School of Mathematical Sciences, Hefei 230601, Anhui, China

^*Corresponding author: Weixian Sun
^*Corresponding author: Weixian Sun

Revised: September 2023

Early access: January 2024

Published: August 2024

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Abstract

In this paper, we establish the global regularity for the two-dimensional incompressible magneto-micropolar equations with almost Laplacian magnetic diffusion and Laplacian micro-rotational diffusion, but without kinematic dissipation. The key arguments are based on the maximal regularity property of the generalized heat operators and a combined quantity. For the two-dimensional incompressible magneto-micropolar equations with only Laplacian magnetic diffusion and Laplacian micro-rotational diffusion, we derive an improved regularity criterion which is less restrictive than the classical Beale-Kato-Majda regularity criterion. Consequently, our results improve and generalize the previous works.

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Mathematics Subject Classification: Primary: 35Q35, 35B65, 76A10; Secondary: 76B03.

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