A weak- $$L^{p}$$ Prodi–Serrin type regularity criterion for the micropolar fluid equations in terms of the pressure

Abstract

This paper is devoted to investigating regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. More precisely, we mainly proved that the weak solution is regular on (0, T] provided that either the norm \(\left\| \pi \right\| _{L^{\alpha ,\infty }(0,T;L^{\beta ,\infty }(\mathbb {R}^{3}))}\) with \(\frac{2}{\alpha }+ \frac{3}{\beta }=2\) and \(\frac{3}{2}<\beta <\infty \) or \(\left\| \nabla \pi \right\| _{L^{\alpha ,\infty }(0,T;L^{\beta ,\infty }(\mathbb {R} ^{3}))}\) with \(\frac{2}{\alpha }+\frac{3}{\beta }=3\) and \(1<\beta <\infty \) is sufficiently small.