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.


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


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