Turing complete Navier-Stokes steady states via cosymplectic geometry
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909682783748096 |
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| author | Dyhr, Søren González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel |
| author_facet | Dyhr, Søren González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel |
| contents | 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 $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Turing complete Navier-Stokes steady states via cosymplectic geometry Dyhr, Søren González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel Differential Geometry Computational Complexity Analysis of PDEs Dynamical Systems Symplectic Geometry 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 $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds. |
| title | Turing complete Navier-Stokes steady states via cosymplectic geometry |
| topic | Differential Geometry Computational Complexity Analysis of PDEs Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2507.07696 |