Session S22 - Deterministic and probabilistic aspects of nonlinear evolution equations

Wednesday, July 14, 16:00 ~ 16:30 UTC-3

RIEMANN’S NON-DIFFERENTIABLE FUNCTION AND THE BINORMAL CURVATURE FLOW

Luis Vega

BCAM- University of the Basque Country, Spain   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We make 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 non- linear geometric interpretation. We recall that the binormal flow is a standard model for the evolution of vortex filaments. We prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior. Finally, we show that this behavior falls within the multifractal formalism of Frisch and Parisi, which is conjectured to govern turbulent fluids.

Joint work with Valeria Banica (Sorbonne U., Paris, France).

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