Global well-posedness for the incompressible MHD equations with variable viscosity and conductivity

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• 作者：Fei Chen^a ; ^{feichenscut@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yongsheng Li^a ; ^{yshli@scut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yongye Zhao^b ; ^{yongyezhao@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Incompressible MHD equations ; Variable viscosity and conductivity ; Strong solutions ; Global existence ; Large-time behavior
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：1051-1071
• 全文大小：446 K

文摘

In this paper, we consider the initial-boundary value problem of the incompressible MHD equations with variable viscosity and conductivity in a smooth bounded domain class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306552&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306552&_rdoc=1&_issn=0022247X&md5=9b16cd20993d958d86e552ca9a5ac796" title="Click to view the MathML source">Ω⊂R³class="mathContainer hidden">class="mathCode">$\mathrm{\Omega }\subset {\mathbb{R}}^3$. We establish the global well-posedness of strong solutions in both non-vacuum and vacuum cases when the initial velocity field and magnetic field are suitably small in some sense with arbitrarily large initial density. In addition, we also get some results of the large-time behavior in both two cases. Our results generalize some previous results in some sense.