Riemann's non-differentiable function and the binormal curvature flow

Riemann's non-differentiable function and the binormal curvature flow

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Valeria Banica, Sorbonne Université

Zoom link: https://princeton.zoom.us/j/92147928280

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In this talk I shall present a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a non-obvious nonlinear geometric interpretation. I will first recall the fact that that the binormal flow is a standard model for the evolution of vortex filaments. Then I shall prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior, that moreover are shown to fall within the multifractal formalism of Frisch and Parisi, which is conjectured to govern turbulent fluids. This result is a joint work with Luis Vega.