Uniform regularity and vanishing dissipation limit for the incompressible magneto-micropolar fluid equations with transverse magnetic field

Lingqi Liu; Limei Li; Yuanming Xu; Lingqi Liu; Limei Li; Yuanming Xu

doi:10.3934/math.2025925

AIMS Mathematics

2025, Volume 10, Issue 9: 20715-20741. doi: 10.3934/math.2025925

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Research article

Uniform regularity and vanishing dissipation limit for the incompressible magneto-micropolar fluid equations with transverse magnetic field

1.
School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, China
2.
Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610068, China

Received: 21 May 2025 Revised: 07 July 2025 Accepted: 16 July 2025 Published: 09 September 2025
MSC : 35Q35, 76W05, 35B40

This paper explores the influence of a transverse magnetic field at the boundary and studies the vanishing dissipation limit of the incompressible magneto-micropolar fluid equations in a half-space. We prove that the solutions remain uniformly bounded, both in the conormal Sobolev norms and the $ L^{\infty} $ norm, over a fixed time interval, independent of the dissipative coefficients. As a result, we establish the convergence of the dissipative magneto-micropolar fluid equations to the corresponding non-dissipative equations in the $ L^{\infty} $ norm. Additionally, our analysis provides uniform regularity energy estimates as the dissipative coefficients tend to zero. This shows that the strong boundary layer can still be prevented by the transverse magnetic field, even with the magnetic diffusion.
- magneto-micropolar fluid equations,
- vanishing dissipation limit,
- conormal Sobolev estimate
Citation: Lingqi Liu, Limei Li, Yuanming Xu. Uniform regularity and vanishing dissipation limit for the incompressible magneto-micropolar fluid equations with transverse magnetic field[J]. AIMS Mathematics, 2025, 10(9): 20715-20741. doi: 10.3934/math.2025925

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Abstract

This paper explores the influence of a transverse magnetic field at the boundary and studies the vanishing dissipation limit of the incompressible magneto-micropolar fluid equations in a half-space. We prove that the solutions remain uniformly bounded, both in the conormal Sobolev norms and the $ L^{\infty} $ norm, over a fixed time interval, independent of the dissipative coefficients. As a result, we establish the convergence of the dissipative magneto-micropolar fluid equations to the corresponding non-dissipative equations in the $ L^{\infty} $ norm. Additionally, our analysis provides uniform regularity energy estimates as the dissipative coefficients tend to zero. This shows that the strong boundary layer can still be prevented by the transverse magnetic field, even with the magnetic diffusion.

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