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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
\[ \pi\in L^q(0,T;B_{p,\infty}^r(\mathbb R^3)), \quad \frac 2q+\frac 3p= 2+r,\quad \frac{3}{2+r}<p<\infty,\quad -1<r\leq 1, \]
then the weak solution \((u,w)\) becomes a regular solution on \((0,T]\). The methods are based on the innovative function decomposition technique.

MSC:

35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
35D30 Weak solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
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References:

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