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Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations. (English) Zbl 1137.76071
Summary: We study the magneto-micropolar fluid equations in $\mathbb R^{3}$, prove the existence of strong solution with initial data in $H^s(\mathbb R^3)$ for $s> \frac 3 2$, and set up its blow-up criterion. The tool we mainly use is Littlewood-Paley decomposition, by which we obtain a Beale-Kato-Majda-type blow-up criterion for smooth solution $(u,\omega , b)$ that relies on the vorticity of velocity $\nabla \times u$ only.

76W05Magnetohydrodynamics and electrohydrodynamics
35Q35PDEs in connection with fluid mechanics
35Q60PDEs in connection with optics and electromagnetic theory
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