Universality of Euler flows and flexibility of Reeb embeddings

The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched programme to address global existence problem for Navier Stokes equations based concept universality. Inspired this proposal, in article we prove that stationary exhibit several universality features. More precisely, show any non-autonomous compact can be extended smooth solution some possibly higher dimension. solutions construct are Beltrami type, being they exist all time. Using result, establish Turing completeness steady flows,i.e., there encode universal machine and, particular, these have undecidable trajectories. Our proofs deepen correspondence between contact topology hydrodynamics, which key Reeb flows their counterparts. An essential ingredient proofs, interest itself, novel flexibility theorem embeddings terms h-principle geometry, unveils flexible behavior flows. These results viewed as lending support intuition extremely complicated nature.