Turing complete Navier–Stokes steady states via cosymplectic geometry
Abstract
In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian three-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic one-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 one-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Control and Stability of Dynamical Systems
Navier-Stokes equation solutions
Publication details
- Journal / source
- PNAS Nexus
- Publisher
- Oxford University Press (OUP)
- Volume
- 5
- Issue
- 5
- Pages
- pgag131–pgag131
- Publication date
- 17 April 2026
- Language
- EN