Year: 2023
Author: Xiangao Liu, Yueli Liu, Zixuan Liu
Communications in Mathematical Research , Vol. 39 (2023), Iss. 1 : pp. 107–135
Abstract
The regularity for 3-D MHD equations is considered in this paper. It is proved that the solutions $(v,B,p)$ are Hölder continuous if the velocity field $v\in L^∞(0,T;L^{3,∞}_x (\mathbb{R}^3))$ with local small condition $$r^{−3}|\{ x∈B_r(x_0):|v(x,t_0)|>εr^{−1}\}|≤\varepsilon$$ and the magnetic field $B∈L^ ∞(0,T;VMO^{−1} (\mathbb{R}^3))$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0048
Communications in Mathematical Research , Vol. 39 (2023), Iss. 1 : pp. 107–135
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Lorentz space backward uniqueness MHD equations.