2020/12/23 by Robert Cardona, Eva Miranda, Daniel Peralta-Salas +2 · 1 voice · 3 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #advanced mathematical theories #Quantum chaos and dynamical systems
paper · pdf · doi:10.1073/pnas.2026818118
4, 199 (1991)] asked if hydrodynamics is capable of performing computations. More recently, Tao launched a program based on the Turing completeness of the Euler equations to address the blow-up problem in the Navier-Stokes equations. In this direction, the undecidability of some physical systems has been studied in recent years, from the quantum gap problem to quantum-field theories. To the best of our knowledge, the existence of undecidable particle paths of three-dimensional fluid flows has remained an elusive open problem since Moore's works in the early 1990s. In this article, we construct a Turing complete stationary Euler flow on a Riemannian [Formula: see text] and speculate on its implications concerning Tao's approach to the blow-up problem in the Navier-Stokes equations.