### Electronic Research Archive

2021, Issue 1: 1625-1639. doi: 10.3934/era.2020083

# Regularity criteria for weak solutions of the Magneto-micropolar equations

• Received: 01 January 2020 Revised: 01 April 2020 Published: 24 August 2020
• Primary: 76W05, 35D30, 35B65, 35Q30

• In this paper, we show that a weak solution $(\mathbf{u},\mathbf{w},\mathbf{b})(\cdot,t)$ of the magneto-micropolar equations, defined in $[0,T)$, which satisfies $\nabla u_3, \nabla_{h} \mathbf{w}, \nabla_{h} \mathbf{b}$ $\in L^{\frac{32}{7}}(0,T;$ $L^2(\mathbb{R}^3))$ or $\partial_3 u_3, \partial_3 \mathbf{w}, \partial_3 \mathbf{b} \in L^{\infty}(0,T;L^2(\mathbb{R}^3))$, is regular in $\mathbb{R}^3\times(0,T)$ and can be extended as a $C^\infty$ solution beyond $T$.

Citation: Jens Lorenz, Wilberclay G. Melo, Suelen C. P. de Souza. Regularity criteria for weak solutions of the Magneto-micropolar equations[J]. Electronic Research Archive, 2021, 29(1): 1625-1639. doi: 10.3934/era.2020083

### Related Papers:

• In this paper, we show that a weak solution $(\mathbf{u},\mathbf{w},\mathbf{b})(\cdot,t)$ of the magneto-micropolar equations, defined in $[0,T)$, which satisfies $\nabla u_3, \nabla_{h} \mathbf{w}, \nabla_{h} \mathbf{b}$ $\in L^{\frac{32}{7}}(0,T;$ $L^2(\mathbb{R}^3))$ or $\partial_3 u_3, \partial_3 \mathbf{w}, \partial_3 \mathbf{b} \in L^{\infty}(0,T;L^2(\mathbb{R}^3))$, is regular in $\mathbb{R}^3\times(0,T)$ and can be extended as a $C^\infty$ solution beyond $T$.

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