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

[Moved Online] Recent Developments in Fluid Dynamics April 12, 2021 - April 30, 2021

April 15, 2021 (11:00 AM PDT - 11:50 AM PDT)
Speaker(s): Luis Vega (Universidad del País Vasco/Euskal Herriko Unibertsitatea)
Location: MSRI: Online/Virtual
Tags/Keywords
  • RIEMANN’S NON-DIFFERENTIABLE FUNCTION

  • binormal flow

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Riemann's Non-Differentiable Function and the Binormal Curvature Flow

Abstract

In a joint work with Valeria Banica, 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. If time permits, I will also mention some recent results on intermittency in the context of the linear Schrödinger equation.

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Riemann's Non-Differentiable Function and the Binormal Curvature Flow

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