Luis Vega: The binormal flow and the evolution of viscous vortex filaments

 I’ll present the so called Localized Induction Approximation that de- scribes the dynamics of a vortex filament according to the Binormal Curvature Flow (BF). I’ll give a result about the desingularization of the Biot-Savart in- tegral proved with Marco A. Fontelos within the framework of Navier-Stokes equations. Some particular examples regarding BF obtained with Valeria Ban- ica will be also considered. These examples allow to connect BF with the so- called Riemann non-differentiable function and the Frisch-Parisi approach to turbulence.