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Regularity of weak solutions to magneto-micropolar fluid equations. (English) Zbl 1240.35421
Summary: In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in $$\mathbb R^3$$. We obtain the classical blow-up criteria for smooth solutions $$(u,\omega, b)$$, i.e., $$u\in L^q(0,T;L^p(\mathbb R^3))$$ for $$\frac 2q+\frac 3p\leq 1$$ with $$3<p\leq \infty, u\in C([0,T); L^3(\mathbb R^3))$$ or $$\nabla u\in L^q(0,T;L^p)$$ for $$\frac 32<p\leq \infty$$ satisfying $$\frac 2q+\frac 3p\leq 2$$. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity $$u$$ of the fluid. In the end-point case $$p=\infty$$, the blow-up criteria can be extended to more general spaces $$\nabla u\in L^1(0,T; \dot{B}^0_{\infty,\infty}(\mathbb R^3))$$.

MSC:
 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs 35D30 Weak solutions to PDEs 35B44 Blow-up in context of PDEs 76W05 Magnetohydrodynamics and electrohydrodynamics
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