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Turing complete Navier–Stokes steady states via cosymplectic geometry

Year: 2026
Type: article
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.
Source: PNAS Nexus
DOI: 10.1093/pnasnexus/pgag131
Institutions: Centre de Recerca Matemàtica, Universitat Politècnica de Catalunya, Universidad Complutense de Madrid, Consejo Superior de Investigaciones Científicas, Institute of Mathematical Sciences, Universidad Carlos III de Madrid
Language: English
Open Access status: gold
Estimated APC paid: $4,202
Funders: Fundación BBVA, “la Caixa” Foundation, Centres de Recerca de Catalunya, Deutsche Forschungsgemeinschaft, Generalitat de Catalunya, Institució Catalana de Recerca i Estudis Avançats, Ministerio de Ciencia e Innovación, Banco Bilbao Vizcaya Argentaria, Agencia Estatal de Investigación
Awards: G1175115578, G1359248042, G148081399, G1868664240, G1908868068, G2064873908, G2262748287, G2462415295, G2756433129, G294895050, G3005324705, G300979063, G3261693824, G34346518, G3480869486, G3522231704, G3546882995, G3860215346, G4228227490, G425668148, G4526231891, G464105488, G4684923497, G5080475149, G5178665745, G5653253907, G5806516646, G6325762137, G6656126374, G675673985, G69051668, G7084143925, G7434936867, G7466406081, G7476827183, G7549035430, G787121397, G7915813472, G84477964, G8522095481, G8637226926
OpenAlex ID: W4416285666
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