The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In this talk we will discuss universality properties of the stationary solutions to the Euler equations. The study of these universality features was suggested by Tao as a novel way to address the problem of global existence for Euler and Navier-Stokes. Universality of the Euler equations for stationary solutions can be proved using using a contact mirror which reflects a Beltrami flow as a Reeb vector field.
This contact mirror permits the use of advanced geometric techniques such as the h-principle in fluid dynamics.