In this talk I will first sketch the derivation of LIA (Local Induction Approximation) as a model for the dynamics of vortex filaments in 3-D fluids. Then I will describe its link with the classical continuous Heisenberg model and with the 1-D cubic Schrödinger equation. Finally I shall present some recent results on solutions generating a singularity in finite time.

Jacques-Louis Lions (Sorbonne)