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Remarks on the regularity criterion of the 3D micropolar fluid flows in terms of the pressure. (English) Zbl 1210.35189

Summary: We study the regularity criterion of weak solutions to the three-dimensional (3D) micropolar fluid flows. It is proved that if the pressure satisfies

πL q (0,T;B p, r ( 3 )),2 q+3 p=2+r,3 2+r<p<,-1<r1,

then the weak solution (u,w) becomes a regular solution on (0,T]. The methods are based on the innovative function decomposition technique.

MSC:
35Q35PDEs in connection with fluid mechanics
76W05Magnetohydrodynamics and electrohydrodynamics
35D30Weak solutions of PDE
35B65Smoothness and regularity of solutions of PDE
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