Vortex reconnections in classical and quantum fluids

Abstract We review recent rigorous results on the phenomenon of vortex reconnection in classical and quantum fluids. In context Navier–Stokes equations $$\mathbb {T}^3$$ T 3 we show existence global smooth solutions that exhibit creation destruction lines arbitrarily complicated topologies. Concerning fluids, prove for any initial final configurations vortices, way transforming one into other, there is an condition whose associated solution to Gross–Pitaevskii equation realizes this specific scenario. Key these inverse localization principle Beltrami fields a approximation theorem linear Schrödinger equation.