Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$
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@Article{CMR-39-107,
author = {Liu , XiangaoLiu , Yueli and Liu , Zixuan},
title = {Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$},
journal = {Communications in Mathematical Research },
year = {2022},
volume = {39},
number = {1},
pages = {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 $B∈L^ ∞(0,T;VMO^{−1} (\mathbb{R}^3))$.
}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0048}, url = {http://global-sci.org/intro/article_detail/cmr/21080.html} }
TY - JOUR
T1 - Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$
AU - Liu , Xiangao
AU - Liu , Yueli
AU - Liu , Zixuan
JO - Communications in Mathematical Research
VL - 1
SP - 107
EP - 135
PY - 2022
DA - 2022/10
SN - 39
DO - http://doi.org/10.4208/cmr.2021-0048
UR - https://global-sci.org/intro/article_detail/cmr/21080.html
KW - Lorentz space, backward uniqueness, MHD equations.
AB -
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 $B∈L^ ∞(0,T;VMO^{−1} (\mathbb{R}^3))$.
Liu , XiangaoLiu , Yueli and Liu , Zixuan. (2022). Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$.
Communications in Mathematical Research . 39 (1).
107-135.
doi:10.4208/cmr.2021-0048
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