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Regularity criteria for the 3D magnetic Bénard equations without thermal diffusion in terms of pressure
Mathematical Methods in the Applied Sciences ( IF 2.1 ) Pub Date : 2020-09-16 , DOI: 10.1002/mma.6899
Dongxiang Chen 1 , Fangfang Jian 1 , Xiaoli Chen 1
Affiliation  

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 2 0 , T ; L 3 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 L 9 2 r 2 r 0 , T ; L 3 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.

中文翻译:

在压力方面没有热扩散的3D磁性Bénard方程的正则条件

在本文中,作者获得了一些新的爆破判据,用于无压力扩散的三维磁性Bénard方程的光滑解。我们证明 π 大号 2 0 Ť ; 大号 3 [R [R 3 0 <  ř  ≤1 ,则强解Û,  b,  θ到磁性贝纳德漩涡方程可以延长超过时间 Ť = Ť 。同时,我们还表明 π 大号 9 - 2 [R 2 [R 0 Ť ; 大号 3 [R [R 3 0 <  ř  ≤1 ,溶液Û,  b,  θ,也可以平滑地延伸超过 Ť = Ť 。最后,通过仅在压力场上施加一些生长条件,我们还获得了有关Morrey空间,乘数空间,BMO空间和Besov空间的规则性标准。
更新日期:2020-09-16
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