A New Pressure Regularity Criterion of the Three-Dimensional Micropolar Fluid Equations

Abstract

This paper concerns the regularity criterion of the weak solutions to the three-dimensional (3D) micropolar fluid equations in terms of the pressure. It is proved that if one of the partial derivatives of pressure satisfies ${\partial }_3\pi \in L^p(0,T;L^q({\mathbf{\text{R}}}^3))$ with , then the weak solution of the micropolar fluid equations becomes regular on $(\mathrm{0},T]$.