Turing complete Navier–Stokes steady states via cosymplectic geometry
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.
Authors
- Eva Miranda (ORCID: https://orcid.org/0000-0001-9518-5279)
- Ángel González-Prieto (ORCID: https://orcid.org/0000-0003-2326-6752)
- Daniel Peralta‐Salas (ORCID: https://orcid.org/0000-0001-5567-8538)
- Søren Dyhr
Institutions
- Universidad Complutense de Madrid (ES)
- Consejo Superior de Investigaciones Científicas (ES)
- Centre de Recerca Matemàtica (ES)
- FC Barcelona (ES)
- Institute of Mathematical Sciences (ES)
- Universidad Carlos III de Madrid (ES)
- Universidad Autónoma de Madrid (ES)
- Universitat Politècnica de Catalunya (ES)
Publication Details
- Journal
- PNAS Nexus
- Published
- 2026-04-17
- DOI
- https://doi.org/10.1093/pnasnexus/pgag131
- Primary Topic
- Stability and Controllability of Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Fundación BBVA
- “la Caixa” Foundation
- Deutsche Forschungsgemeinschaft
- Institució Catalana de Recerca i Estudis Avançats
- Ministerio de Ciencia e Innovación
- Banco Bilbao Vizcaya Argentaria
- Agencia Estatal de Investigación