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A regularity criterion for the 3D magneto-micropolar fluid equations in Triebel-Lizorkin spaces. (English) Zbl 1209.35105

Summary: We consider the regularity criterion for the 3D magneto-micropolar fluid equations in Triebel-Lizorkin spaces. It is proved that if \(\nabla{\mathbf u}\in L^p(0,T;\dot F_{q,2q/3}^0)\) with
\[ \tfrac 2p+\tfrac 3q=2, \quad 3/2<q\leq\infty, \]
then the solution remains smooth in \((0,T)\). As a corollary, we obtain the classical Beal-Kato-Majda criterion, that is, the condition
\[ \nabla\times{\mathbf u}\in L^1(0,T;\dot B_{\infty,\infty}^0), \]
ensures the smoothness of the solution.

MSC:

35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
35B65 Smoothness and regularity of solutions to PDEs
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