Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2022

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

Résumé

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.

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hal-02917039 , version 1 (18-08-2020)

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  • HAL Id : hal-02917039 , version 1

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Valeria Banica, Luis Vega. Riemann's non-differentiable function and the binormal curvature flow. Archive for Rational Mechanics and Analysis, 2022, 244, pp.501-540. ⟨hal-02917039⟩
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