Existence theorem and blow-up criterion of the strong solutions to the Magneto-micropolar fluid equations

Abstract

In this paper we study the magneto-micropolar fluid equations in ${\mathbb{R}}^3$, prove the existence of the strong solution with initial data in $H^s({\mathbb{R}}^3)$ for $s>3/2$, 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 $(u,\omega ,b)$ which relies on the vorticity of velocity $\nabla \times u$ only.

19pages

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• Two problems in Partial Differential Equations (in Portuguese)
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