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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 $\Bbb R^3$. We obtain the classical blow-up criteria for smooth solutions $(u,\omega, b)$, i.e., $u\in L^q(0,T;L^p(\Bbb R^3))$ for $\frac 2q+\frac 3p\leq 1$ with $3<p\leq \infty, u\in C([0,T); L^3(\Bbb R^3))$ 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 $\nabla u\in L^1(0,T; \dot{B}^0_{\infty,\infty}(\Bbb R^3))$.

35Q35PDEs in connection with fluid mechanics
35B65Smoothness and regularity of solutions of PDE
35D30Weak solutions of PDE
35B44Blow-up (PDE)
76W05Magnetohydrodynamics and electrohydrodynamics
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