Turing complete Navier-Stokes steady states via cosymplectic geometry
Søren Dyhr, Ángel González-Prieto, Eva Miranda and Daniel Peralta-Salas
本文在特定黎曼3-流形上构造了纳维-斯托克斯方程的稳态解，这些解展现出图灵完备性，即能够执行通用计算。这种普适性出现在允许非零调和1-形式的流形上，从而表明只要底层几何满足温和的上同调条件，计算普适性不会受到粘性的阻碍。证明利用了非零调和1-形式与余辛几何之间的对应关系，这一关系扩展了接触流形上Beltrami场与Reeb流之间的经典对应。
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...
