Self-binormal solutions of the Localized Induction Approximation:   Singularity formation
  We investigate the formation of singularities in a self-similar form of regular solutions of the Localized Induction Approximation (also referred as to the binormal flow). This equation appears as an approximation model for the self-induced motion of a vortex filament in an inviscid incompressible fluid. The solutions behave as 3d-logarithmic spirals at infinity.   The proofs of the results are strongly based on the existing connection between the binormal flow and certain Schr\"odinger equations. 
Susana Gutierrez (University of Edinburgh), Luis Vega (Basque Country   University)