Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space

We prove local regularity condition for a suitable weak solution to 3D MHD equations. Precisely, if a solution satisfies $u, b \in L^{\infty}(-(\frac{4}{3})^2, 0;L^{3, q}(B_{\frac{3}{4}}))$, $q\in (3, \infty)$ in Lorentz space, then $(u, b)$ is Hölder continuous in the closure of the set $Q_{\frac{1...

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Main Author:	Jae-Myoung Kim
Format:	Article
Language:	English
Published:	AIMS Press 2021-01-01
Series:	AIMS Mathematics
Subjects:	local regularity condition suitable weak solution 3d mhd equations
Online Access:	http://www.aimspress.com/article/doi/10.3934/math.2021148?viewType=HTML

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spelling	doaj-3add74ea50cf4053a6159020ec0751192021-01-07T02:26:50ZengAIMS PressAIMS Mathematics2473-69882021-01-01632440245310.3934/math.2021148Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz spaceJae-Myoung Kim0Department of Mathematics Education, Andong National University, Andong 36729, Republic of KoreaWe prove local regularity condition for a suitable weak solution to 3D MHD equations. Precisely, if a solution satisfies $u, b \in L^{\infty}(-(\frac{4}{3})^2, 0;L^{3, q}(B_{\frac{3}{4}}))$, $q\in (3, \infty)$ in Lorentz space, then $(u, b)$ is Hölder continuous in the closure of the set $Q_{\frac{1}{2}}$.http://www.aimspress.com/article/doi/10.3934/math.2021148?viewType=HTMLlocal regularity conditionsuitable weak solution3d mhd equations
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jae-Myoung Kim
spellingShingle	Jae-Myoung Kim Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space AIMS Mathematics local regularity condition suitable weak solution 3d mhd equations
author_facet	Jae-Myoung Kim
author_sort	Jae-Myoung Kim
title	Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space
title_short	Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space
title_full	Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space
title_fullStr	Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space
title_full_unstemmed	Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space
title_sort	local interior regularity for the 3d mhd equations in nonendpoint borderline lorentz space
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2021-01-01
description	We prove local regularity condition for a suitable weak solution to 3D MHD equations. Precisely, if a solution satisfies $u, b \in L^{\infty}(-(\frac{4}{3})^2, 0;L^{3, q}(B_{\frac{3}{4}}))$, $q\in (3, \infty)$ in Lorentz space, then $(u, b)$ is Hölder continuous in the closure of the set $Q_{\frac{1}{2}}$.
topic	local regularity condition suitable weak solution 3d mhd equations
url	http://www.aimspress.com/article/doi/10.3934/math.2021148?viewType=HTML
work_keys_str_mv	AT jaemyoungkim localinteriorregularityforthe3dmhdequationsinnonendpointborderlinelorentzspace
_version_	1724346841737199616

Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space

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