Uniform regularity and vanishing viscosity limit for the incompressible non-resistive magneto-micropolar equations

Abstract

In this paper, we consider the vanishing viscosity limit for the incompressible non-resistive magneto-micropolar equations on the half-space with no-slip boundary condition (3). We prove that the vanishing viscosity limit is uniform over a time interval, which indicates that the incompressible non-resistive magneto-micropolar equations with the no-slip boundary condition have a strong solution and the solution is uniformly bounded in both the conormal Sobolev norm and $L^{\mathrm{\infty }}$ norm. As a direct result, we obtain the vanishing viscosity limit for the incompressible non-resistive magneto-micropolar equations by a strong compactness argument.

Keywords:

• Incompressible non-resistive magneto-micropolar equations
• uniform regularity
• vanishing viscosity limit
• no-slip boundary condition

2020 Mathematics Subject Classifications:

• 35Q35
• 35M33
• 35B40

Acknowledgements

The authors express much gratitude to Professor Ting Zhang for his support.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Fujian Provincial Youth Education and Scientific Research Project under Grant (No. JAT200028) and the Natural Science Foundation of Fujian Province (No. 2021J01614).