2025/07/10 by Dyhr, Søren, González-Prieto, Ángel, Miranda, Eva +1 · 1 citation
#Analysis of PDEs (math.AP) #Computational Complexity (cs.CC) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2507.07696
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.