Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$

Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$

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.

Author Details

Xiangao Liu

Yueli Liu

Zixuan Liu