{"title":"三维可压缩粘性无阻力MHD系统的全局小解","authors":"Jiahong Wu, Xiaoping Zhai","doi":"10.1142/s0218202523500574","DOIUrl":null,"url":null,"abstract":"Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is currently available for this 3D MHD system in the whole space [Formula: see text] or the periodic box [Formula: see text] even when the initial data is small or near a steady-state solution. This paper presents a global existence and stability result for smooth solutions to this 3D MHD system near any background magnetic field satisfying a Diophantine condition.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"45 7","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Global small solutions to the 3D compressible viscous non-resistive MHD system\",\"authors\":\"Jiahong Wu, Xiaoping Zhai\",\"doi\":\"10.1142/s0218202523500574\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is currently available for this 3D MHD system in the whole space [Formula: see text] or the periodic box [Formula: see text] even when the initial data is small or near a steady-state solution. This paper presents a global existence and stability result for smooth solutions to this 3D MHD system near any background magnetic field satisfying a Diophantine condition.\",\"PeriodicalId\":18311,\"journal\":{\"name\":\"Mathematical Models and Methods in Applied Sciences\",\"volume\":\"45 7\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Models and Methods in Applied Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218202523500574\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Models and Methods in Applied Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218202523500574","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Global small solutions to the 3D compressible viscous non-resistive MHD system
Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is currently available for this 3D MHD system in the whole space [Formula: see text] or the periodic box [Formula: see text] even when the initial data is small or near a steady-state solution. This paper presents a global existence and stability result for smooth solutions to this 3D MHD system near any background magnetic field satisfying a Diophantine condition.
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