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Regularity criteria for the 3D magnetic Bénard equations without thermal diffusion in terms of pressure
Author(s) -
Chen Dongxiang,
Jian Fangfang,
Chen Xiaoli
Publication year - 2020
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.6899
Subject(s) - mathematics , space (punctuation) , magnetic field , besov space , multiplier (economics) , diffusion , mathematical analysis , thermal , physics , thermodynamics , functional analysis , computer science , chemistry , biochemistry , macroeconomics , quantum mechanics , interpolation space , economics , gene , operating system
In this paper, the authors obtain some new blow‐up criteria for the smooth solutions to the three‐dimensional magnetic Bénard equations without thermal diffusion in terms of pressure. We prove that if π ∈ L 20 , T ; L3 r( R 3 )with 0 < r ≤ 1 , then the strong solutions ( u , b , θ ) to the magnetic Bénard equations can be extended beyond time t = T . Meanwhile, we also show that provided that ∇ π ∈ L9 − 2 r 2 r0 , T ; L3 r( R 3 )with 0 < r ≤ 1 , the solutions ( u , b , θ ) can also be extended smoothly beyond t = T . Finally, we also obtain the regularity criteria on Morrey space, multiplier space, BMO space, and Besov space by imposing some growth conditions only on the pressure field.