A new Beale-Kato-Majda criteria for the 3D magneto-micropolar fluid equations in the Orlicz-Morrey space

摘要

In this work, we are interested in the study of regularity for the three-dimensional magneto-micropolar fluid equations in Orlicz-Morrey spaces. If the velocity field satisfies u∈L21-r0,T;ML2logPL3rR3 with r∈(0,1) and P>1 or the gradient field of velocity satisfies ?u∈L22-r0, T;ML2logPL3rR3 with r∈(0,2) and P>1, then we show that the solution remains smooth on [0,T]. In view of the embedding L3r?Mp3r?ML2logPL3r with 2 < p < 3 / r and P > 1, we see that our result extends the result of Yuan and that of Gala.