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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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