Dynamics of Steady Euler Flows: New Results

This lecture by the instructor focuses on the dynamics of steady Euler flows, describing the evolution of inviscid and incompressible fluid flows on Riemannian manifolds. Topics covered include ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs in Euler flows. The lecture delves into the characterization of Eulerisable flows, their geometric properties, and the concept of Euler-extendible flows. Furthermore, it explores the universality of Euler flows and their Turing completeness, providing insights into potential blow-up solutions for the Navier-Stokes equations.