Speaker: Francisco Torres De Lizaur, University of Sevilla
Abstract:
In this talk we consider the following non-mixing problem for the 3D Euler equations of ideal hydrodynamics: show that there are pairs of smooth velocity fields, with the same energy and helicity, such that no field close to one can ever evolve into a field close to the other. Here velocity fields are close if their pointwise values, and that of their derivatives up to order k, are similar enough.
Khesin, Kuksin and Peralta-Salas proved this in 2014 for k>=4, KAM theorem being behind the regularity threshold. Proving the same result for k smaller remained an open problem. I will present joint work with Robert Cardona where we prove this for all k>=1, by introducing a new framework that assigns contact geometry invariants to large sets of time-dependent solutions on any 3-manifold with any fixed metric.