Prof. Yoshi Kimura, Graduate School of Mathematics, Nagoya University, Japan

"Vortex reconnection as a candidate for a finite time singularity of the Navier-Stokes equations"

Abstract: Regularity/Singularity of the Navier-Stokes equations is one of the 7 millennium prize problems of the Clay Mathematical Institute. As a candidate for the solutions to that problem, vortex collisions, or eventual vortex reconnections have been investigated widely. Recently, a dynamical system is proposed which describes a vortex reconnection of two vortex rings located symmetrically on two tilted planes initially. In this talk, after showing the introduction of the problem, we will present some results of analysis and simulations of the dynamical system.