Global well-posedness for 3D incompressible magneto-micropolar fluids without resistivity and spin viscosity in strip domains

Youyi Zhao

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arXiv · 2605.21927

Global well-posedness for 3D incompressible magneto-micropolar fluids without resistivity and spin viscosity in strip domains

Youyi Zhao

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Abstract

The global existence of classical solutions to the 3D compressible magneto-micropolar fluid system without resistivity and spin viscosity in a strip domain was recently established by Feng, Hong, and Zhu [Sci. China Math., 2024]. While Lin and Xiang [Sci. China Math., 2020] established global well-posedness for the 2D incompressible counterpart, the global well-posedness for the 3D incompressible case remains open. The analysis is rendered difficult by three major obstacles which are further compounded in the 3D case: the degeneracy induced by the lack of magnetic diffusion and spin viscosity; the coupling between micro-rotation and velocity fields characterized by a non-dissipative anti-symmetric structure; and the interaction between the velocity, magnetic field, and pressure, where the pressure acts as a non-state variable. In this paper, by adapting the two-layer energy method of Guo and Tice [Arch. Ration. Mech. Anal., 2013] and the techniques employed in Feng et al., together with refined trace estimates, we overcome these difficulties and establish the global well-posedness of classical solutions to the 3D incompressible magneto-micropolar fluid system without resistivity and spin viscosity in a strip domain. Moreover, we demonstrate the algebraic time-decay of solutions toward the equilibrium.

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Youyi Zhao. 2026-05-21. Global well-posedness for 3D incompressible magneto-micropolar fluids without resistivity and spin viscosity in strip domains. https://arxiv.org/abs/2605.21927

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