All Questions

How can the vortex filament equation $$\partial_t \chi = \partial_s \chi \wedge \partial_{ss} \chi,$$ where $\chi(t,s)$ is a curve in $\mathbb R^3$, be derived from the Euler equation $$\partial_t \...

Disclaimer. I expect this is a highly open problem, but maybe I'm wrong and someone has come up with some answers besides those given here. In any case, all information appreciated, thanks! Definition....