Turing completeness and universality of steady Euler flows

Abstract: I will review recents results on the Turing completeness and universality of steady solutions to the Euler equations. In particular, I will show the existence of three-dimensional fluid flows exhibiting undecidable trajectories and discuss other universality features such as embeddability of diffeomorphisms into steady Euler states. These results are motivated by Tao's programme to address the blow-up problem for the Navier-Stokes equations based on the Turing completeness of the fluid flows. This is based on joint works with Robert Cardona, Eva Miranda and Francisco Presas.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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