Universality of Euler flows and flexibility of Reeb embeddings
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Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/185761
Tipus de documentReport de recerca
Data publicació2019-11-05
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier Stokes equations based on the concept of universality. In this article we prove that the Euler equations exhibit universality features. More precisely, we show that any non autonomous flow on a compact manifold can be extended to a smooth solution of the Euler equations on some Riemannian manifold of possibly higher dimension. The solutions we construct are stationary of Beltrami type, so they exist for all time. Using this result, we establish the Turing completeness of the Euler flows, i.e. that there exist solutions that encode a universal Turing machine. The proofs exploit the correspondence between contact topology and hydrodynamics, which allows us to import the flexibility principles from the contact realm, in the form of holonomic h-principles for isocontact embeddings.
CitacióCardona, R. [et al.]. "Universality of Euler flows and flexibility of Reeb embeddings". 2019.
URL repositori externhttps://arxiv.org/abs/1911.01963
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cardonamirandaperaltapresas.pdf | Preprint | 442,3Kb | Visualitza/Obre |