Vortex reconnections in classical and quantum fluids

We review recent rigorous results on the phenomenon of vortex reconnection in classical and quantum fluids. In the context of the Navier¿Stokes equations in T3 we show the existence of global smooth solutions that exhibit creation and destruction of vortex lines of arbitrarily complicated topologies. Concerning quantum fluids, we prove that for any initial and final configurations of quantum vortices, and any way of transforming one into the other, there is an initial condition whose associated solution to the Gross¿Pitaevskii equation realizes this specific vortex reconnection scenario. Key to prove these results is an inverse localization principle for Beltrami fields and a global approximation theorem for the linear Schrödinger equation.A.E. is supported by the ERC Consolidator Grant 862342. D.P.-S. is supported by the grants MTM PID2019-106715GB-C21 and Europa Excelencia EUR2019-103821 from Agencia Estatal de Investigación (AEI). This work is supported in part by the ICMAT–Severo Ochoa grant CEX2019-000904-S and the grant RED2018-102650-T funded by MCIN/AEI/10.13039/501100011033