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An optimal regularity criterion for the 3D MHD equations in homogeneous Besov spaces
Author(s) -
Guo Zhengguang,
Zhang Shunhang
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.6923
Subject(s) - mathematics , magnetohydrodynamics , homogeneous , mathematical analysis , compressibility , besov space , weak solution , pure mathematics , functional analysis , combinatorics , physics , magnetic field , mechanics , interpolation space , biochemistry , chemistry , quantum mechanics , gene
In this paper, we establish a new regularity criterion for weak solutions to the 3D incompressible MHD equations in terms of two pairs of ( ∂ i u i , ∂ i b i ) ( i = 1,2 , 3 ) . More precisely, it is proved that the weak solution ( u , b ) is smooth on (0, T ] , provided that for some i , j ∈ {1, 2, 3} with i ≠ j , it holds that∂ iu i , ∂ ju j , ∂ ib i , ∂ jb j ∈ L p0 , T ;B ˙q , ∞ 0 ( ℝ 3 ) ,2 p + 3 q = 2 , 3 ≤ q ≤ ∞ .