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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 3 . We obtain the classical blow-up criteria for smooth solutions (u,ω,b), i.e., uL q (0,T;L p ( 3 )) for 2 q+3 p1 with 3<p,uC([0,T);L 3 ( 3 )) or uL q (0,T;L p ) for 3 2<p satisfying 2 q+3 p2. 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=, the blow-up criteria can be extended to more general spaces uL 1 (0,T;B ˙ , 0 ( 3 )).

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