报告人：Yasuhide Fukumoto

报告人的单位: Institute of Mathematics for Industry, Kyushu University, Japan

报告题目: Evolution of a magneto-vortex ring with and without Hall effect

摘要:
A general formula is established for translation speed of a thin toroidal magnetic eddy in a MHD flow. We rely on the method developed by Helmholtz, Lamb, Saffman, Rott and Cantwell. Then we turn to a spherical magnetic eddy, being a fat vortex ring. A family of exact solutions for the axisymmetric poloidal MHD flows found by Hattori and Moffatt (2006) includes Hill's spherical vortex for the classical hydrodynamic situations. The Hall effect is a singular perturbation to the MHD equations, which describe motion of plasmas of being consisting of ions and electrons. We extend their exact solutions to accommodate the Hall effect, and derive two types of exact solutions of the Hall MHD. One is an extension of the MHD Hill's vortex, while the other is a special solution pertaining only to the Hall MHD.