Turing complete steady Navier–Stokes flows on compact 3-manifolds

Determine whether there exists a Turing complete steady solution to the Navier–Stokes equations on some compact Riemannian three-manifold.

Background

The constructions in the paper yield Turing complete stationary solutions of the Euler equations (ideal fluids). Extending these ideas to viscous fluids (Navier–Stokes) is challenging, especially on compact spaces, because robustness under perturbations is impossible in that setting, suggesting viscosity may destroy computational power.

The problem asks whether any steady Navier–Stokes flow on a compact Riemannian 3-manifold can nonetheless be Turing complete, despite the limitations revealed by robustness results.