In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian 3-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic -forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.
Ha! Turing complete Navier-Stokes steady states via cosymplectic geometry.
@gwern perhaps a new addition to your [Surprisingly Turing Complete](https://gwern.net/turing-complete) page.
As the paper notes, this is part of Terry Tao’s proposed strategy for resolving the Navier-Stokes millennium problem.