On regularity criteria for the three-dimensional micropolar fluid equations in the critical Morrey–Campanato space

In this paper, we establish a Serrin-type regularity criterion for the weak solutions to the micropolar fluid equations in R3R3. It is proved that, if the velocity field satisfies one of the following conditions: u∈L21−r(0,T;Ṁ2,3r(R3))or∇u∈L22−r(0,T;Ṁ2,3r(R3)), or the associated pressure satisfies one of the following conditions: p∈L22−r(0,T;Ṁ2,3r(R3))or∇p∈L23−r(0,T;Ṁ2,3r(R3)), then the solution remains smooth on [0,T][0,T].