{"title":"Lorentz空间中三维MHD方程的正则性$L^{3,∞}$","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":"{\"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}","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
摘要
本文考虑了三维MHD方程的正则性,证明了当速度场v∈L∞(0,T;L x (R3))具有局部小条件R∣∣{x∈Br(x0): |v(x,t0)|> ε R−1∣∣≤ε且磁场B∈L∞(0,T;VMO−1(R3))时,解(v,B,p)是Hölder连续的。AMS学科分类:35Q35、76B03、76D03
Regularity for 3-D MHD Equations in Lorentz Space $L^{3,∞}$
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