Riemann’s Non-differentiable Function and the Binormal Curvature Flow

We make a connection between famous analytical object introduced in the 1860s by Riemann, as well some variants of it, and nonlinear geometric PDE, binormal curvature flow. As consequence, this has non-obvious interpretation. recall that flow is standard model for evolution vortex filaments. prove existence solutions with smooth trajectories are close desired to curves multifractal behavior. Finally, we show behavior falls within formalism Frisch Parisi, which conjectured govern turbulent fluids.