The Long Way of a Viscous Vortex Dipole

Watch a 56-minute mathematics conference talk exploring the behavior of viscous vortex dipoles in two-dimensional fluid dynamics. Delve into the analysis of the Navier-Stokes equation with singular initial data representing point vortices with opposite circulations. Learn how approximate solutions are constructed in high Reynolds number scenarios, accounting for streamline deformation and translation speed corrections due to vortex interactions. Understand the application of energy estimates based on Arnold's variational characterization of Euler equation equilibria to demonstrate the validity of approximations over extended time periods with sufficiently small viscosity. Recorded at the "Mathematics of fluids in motion: Recent results and trends" thematic meeting at the Centre International de Rencontres Mathématiques in Marseille, France, this collaborative research presentation includes work with Michele Dolce and Vladimir Sverak.