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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.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory
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