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: