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A new Beale–Kato–Majda criteria for the 3D magneto‐micropolar fluid equations in the Orlicz–Morrey space
Author(s) -
Gala Sadek,
Sawano Yoshihiro,
Tanaka Hitoshi
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2535
Subject(s) - mathematics , embedding , space (punctuation) , vector field , field (mathematics) , mathematical analysis , mathematical physics , pure mathematics , geometry , philosophy , linguistics , artificial intelligence , computer science
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.