{"title":"Global unique solutions for the incompressible MHD equations with variable density and electrical conductivity","authors":"Xueli Ke","doi":"10.1007/s10473-024-0507-2","DOIUrl":null,"url":null,"abstract":"<p>We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data (<i>u</i><sub>0</sub>, <i>B</i><sub>0</sub>) being located in the critical Besov space <span>\\(\\dot{B}_{p,1}^{{-1}+{{2}\\over{p}}}(\\mathbb{R}^{2})\\)</span> (1 < <i>p</i> < 2) and the initial density <i>ρ</i><sub>0</sub> being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"14 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0507-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data (u0, B0) being located in the critical Besov space \(\dot{B}_{p,1}^{{-1}+{{2}\over{p}}}(\mathbb{R}^{2})\) (1 < p < 2) and the initial density ρ0 being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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