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

Research paper by Shu Wang, Jihui Wu

Indexed on: 19 Mar '16Published on: 19 Mar '16Published in: Bulletin of the Malaysian Mathematical Sciences Society



Abstract

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.