Remarks on the Pressure Regularity Criterion of the Micropolar Fluid Equations in Multiplier Spaces

Abstract

This study is devoted to investigating the regularity criterion of weak solutions of the micropolar fluid equations in ${ℝ}^3$. The weak solution of micropolar fluid equations is proved to be smooth on $(0,T]$ when the pressure $\pi (x,t)$ satisfies the following growth condition in the multiplier spaces ${\dot{X}}^r$, . The previous results on Lorentz spaces and Morrey spaces are obviously improved.