An improved regularity criterion for the 3D magneto-micropolar equations in homogeneous Besov space

Abstract

In this paper we consider the regularity criterion for the weak solutions to the 3D incompressible magneto-micropolar equations. We establish an improved regularity criterion for weak solutions in terms of two pairs of (∂iui,∂ibi)(i=1,2,3). More precisely, we show that for some i,j∈{1,2,3} with i≠j, if(∂iui,∂ibi),(∂juj,∂jbj)∈Lp(0,T;B˙q,∞0(R3)),2p+3q=2,3≤q≤∞, then the solution (u,w,b) to the magneto-micropolar equations is smooth on [0,T].