Abstract : Vorticity filaments (one-dimensional structures where vorticity concentrates) play a central role in understanding turbulence generation and energy transfer in fluids. In this talk, I will discuss about how these structures evolve in a viscous fluid. I will consider initial data given by a vorticity measure supported on an infinite smooth curve in R^3. I will show that, for short enough time, the solution consists of a leading-order Lamb–Oseen vortex centered around a curve that evolves according to the binormal flow, a second-order term reflecting the local curvature of the filament, and a small nonlocal correction. For this, I will need to assume that $\Gamma$ , the circulation around the vortex, is sufficiently small.

The talk will be held in person

Venue: DIM seminar room, Beauchef 851, 5th floor.

Zoom: https://uchile.zoom.us/j/93324747064?pwd=bzbZ2ADIpsi2ye6t00fJnwWOLJ4JLy.1