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Constructing Turing complete Euler flows in dimension 3

Authors :
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
Cardona Aguilar, Robert
Miranda Galcerán, Eva
Peralta-Salas, Daniel
Presas, Francisco
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
Cardona Aguilar, Robert
Miranda Galcerán, Eva
Peralta-Salas, Daniel
Presas, Francisco
Publication Year :
2021

Abstract

Published under the PNAS license<br />Can every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning fluid flows, Moore asked in [15] if hydrodynamics is capable of performing computations. More recently, Tao launched a programme 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 [7] to quantum field theories [11]. To the best of our knowledge, the existence of undecidable particle paths of 3D fluid flows has remained an elusive open problem since Moore's works in the early 1990's. In this article we construct a Turing complete stationary Euler flow on a Riemannian S3 and speculate on its implications concerning Tao's approach to the blow up problem in the Navier-Stokes equations.<br />This work was partially supported by ICMAT–Severo OchoaGrant CEX2019-000904-S.<br />Peer Reviewed<br />Postprint (author's final draft)

Details

Database :
OAIster
Notes :
application/pdf, English
Publication Type :
Electronic Resource
Accession number :
edsoai.on1298721658
Document Type :
Electronic Resource