# Surveys/monographs on the vortex filament equation

Where can I find surveys on the mathematical aspects of the vortex filament equation?

In particular, I'm interested in the following topics:

• physical motivation;
• notion of solutions and wellposedness;
• relationship with the Schrödinger equation;
• relationship with Euler and Navier-Stokes equations;
• formation of singularities.

Note 1. Vortex filament equation: $$\partial_t \chi = \partial_s \chi \wedge \partial_{ss} \chi,$$ where $$\chi(t,s)$$ is a curve in $$\mathbb R^3$$.

Note 2. Related questions have been asked at the following links: