Evolution of viscous vortex filaments.

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.

Posted on Aug 12, 2025 in Differential Equations, Seminars