{"title":"Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$","authors":"Xian-gao Liu, Yueli Liu, Zixuan Liu","doi":"10.4208/cmr.2021-0048","DOIUrl":null,"url":null,"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∈L∞(0,T;L x (R 3)) with local small condition r ∣∣ { x∈Br(x0) : |v(x,t0)|> εr −1 ∣∣≤ ε and the magnetic field B∈L∞(0,T;VMO−1(R3)). AMS subject classifications: 35Q35, 76B03, 76D03","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究通讯","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/cmr.2021-0048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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∈L∞(0,T;L x (R 3)) with local small condition r ∣∣ { x∈Br(x0) : |v(x,t0)|> εr −1 ∣∣≤ ε and the magnetic field B∈L∞(0,T;VMO−1(R3)). AMS subject classifications: 35Q35, 76B03, 76D03