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
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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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
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