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Turing universality of the incompressible Euler equations and a conjecture of Moore
dc.contributor.author | Cardona Aguilar, Robert |
dc.contributor.author | Miranda Galcerán, Eva |
dc.contributor.author | Peralta-Salas, Daniel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2022-04-01T11:23:17Z |
dc.date.available | 2022-08-25T00:27:53Z |
dc.date.issued | 2021-08-24 |
dc.identifier.citation | Cardona, R.; Miranda, E.; Peralta-Salas, D. Turing universality of the incompressible Euler equations and a conjecture of Moore. "International mathematics research notices", 24 Agost 2021, vol. 22, núm. 22, p. 18092-18109. |
dc.identifier.issn | 1073-7928 |
dc.identifier.uri | http://hdl.handle.net/2117/365194 |
dc.description.abstract | In this article, we construct a compact Riemannian manifold of high dimension on which the time-dependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent to a certain global solution of the Euler equations entering a certain open set in the space of divergence-free vector fields. In particular, this implies the undecidability of whether a solution to the Euler equations with an initial datum will reach a certain open set or not in the space of divergence-free fields. This result goes one step further in Tao’s programme to study the blow-up problem for the Euler and Navier–Stokes equations using fluid computers. As a remarkable spin-off, our method of proof allows us to give a counterexample to a conjecture of Moore dating back to 1998 on the non-existence of analytic maps on compact manifolds that are Turing complete. |
dc.description.sponsorship | María de Maeztu Programme (MDM-2014-0445) AGAUR grant 2017SGR932 ICMAT–Severo Ochoa grant CEX2019-000904-S |
dc.description.sponsorship | Robert Cardona acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Mar´ıa de Maeztu Programme for Units of Excellence in R& D (MDM-2014-0445) via an FPI grant. Robert Cardona and Eva Miranda are partially supported by the grants MTM2015-69135- P/FEDER and PID2019-103849GB-I00 / AEI / 10.13039/501100011033, and AGAUR grant 2017SGR932. Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia Prize 2016. Daniel Peralta-Salas is supported by the grants MTM PID2019-106715GB-C21 (MICINN) and Europa Excelencia EUR2019-103821 (MCIU). This work was partially supported by the ICMAT– Severo Ochoa grant CEX2019-000904-S. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat |
dc.subject.lcsh | Computer science |
dc.subject.other | Riemannian manifold |
dc.subject.other | Euler equations |
dc.subject.other | Turing complete |
dc.title | Turing universality of the incompressible Euler equations and a conjecture of Moore |
dc.type | Article |
dc.subject.lemac | Informàtica |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.identifier.doi | 10.1093/imrn/rnab233 |
dc.subject.ams | Classificació AMS::68 Computer science::68Q Theory of computing |
dc.relation.publisherversion | https://academic.oup.com/imrn |
dc.rights.access | Open Access |
local.identifier.drac | 32837774 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2015-69135-P/ES/GEOMETRIA Y TOPOLOGIA DE VARIEDADES, ALGEBRA Y APLICACIONES/ |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-103849GB-I00/ES/GEOMETRIA, ALGEBRA, TOPOLOGIA Y APLICACIONES MULTIDISCIPLINARES/ |
local.citation.author | Cardona, R.; Miranda, E.; Peralta-Salas, D. |
local.citation.publicationName | International mathematics research notices |
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