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

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 ∈ L2 1 − r0 , T ; ML 2log P L3 rR 3 with  r ∈ ( 0 , 1 )  and  P > 1 or the gradient field of velocity satisfies ∇ u ∈ L2 2 − r0 , T ; ML 2log P L3 rR 3 with  r ∈ ( 0 , 2 )  and  P > 1 , then we show that the solution remains smooth on [0, T ]. In view of the embeddingL3 r⊂ M p3 r⊂ ML 2log P L3 rwith 2 <  p  < 3 ∕  r and P  > 1, we see that our result extends the result of Yuan and that of Gala. Copyright © 2012 John Wiley & Sons, Ltd.