Property of Solution to Axially Symmetric Incompressible MHD Equations in Three Dimensions

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• 作者：Shu Wang ; Jihui Wu
• 关键词：Incompressible ; MHD ; Axially asymmetric ; Three dimensional
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：173-204
• 全文大小：
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：40

文摘

In this paper, we study the property of solutions to axially symmetric incompressible MHD equations in three dimensions. First, we present the three-dimensional axially symmetric incompressible MHD equations. We propose a new one-dimensional model that approximates the MHD equations along the symmetric axis. This one-dimensional model can construct a family of exact solutions to the three-dimensional MHD equations. Second, we give a family of particular solutions to the three-dimensional and a prior estimates of one-dimensional MHD equations. Finally, we construct a family of global smooth solutions to the three-dimensional MHD equations by applying the one-dimensional solutions.