Vorticity, rotation and symmetry (IV): Complex fluids and the issue of regularity / Vorticité, rotation et symétrie (IV) : fluides complexes et problèmes de régularité

Collection Vorticity, rotation and symmetry (IV): Complex fluids and the issue of regularity / Vorticité, rotation et symétrie (IV) : fluides complexes et problèmes de régularité

Organisateur(s) Danchin, Raphaël ; Farwig, Reinhard ; Neustupa, Jiri ; Penel, Patrick

Date(s) 08/05/2017 - 12/05/2017

URL associée http://conferences.cirm-math.fr/1588.html

00:00:00 / 00:00:00

4 5

Chapitres

The Onsager Theorem

De Camillo de Lellis

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics. Our remark sparked a series of discoveries and works which have gone in several directions. Among them the most notable is the recent proof of Phil Isett of a long-standing conjecture of Lars Onsager in the theory of turbulent flows. In a joint work with László, Tristan Buckmaster and Vlad Vicol we improve Isett's theorem to show the existence of dissipative solutions of the incompressible Euler equations below the Onsager's threshold.

Informations sur la vidéo

Date de captation 10/05/2017
Date de publication 18/05/2017
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19165203
Citer cette vidéo de Lellis, Camillo (10/05/2017). The Onsager Theorem. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19165203
URL https://dx.doi.org/10.24350/CIRM.V.19165203

Domaine(s)

Equations aux dérivées partielles

Bibliographie

Buckmaster, T., De Lellis, C., Székelyhidi, L. Jr., & Vicol, V. (2017). Onsager's conjecture for admissible weak solutions. <arXiv:1701.08678> - https://arxiv.org/abs/1701.08678
De Lellis, C., & Székelyhidi, L. Jr. (2013). Dissipative continuous Euler flows. Inventiones Mathematicae, 193(2), 377-407 - http://dx.doi.org/10.1007/s00222-012-0429-9
Isett, P. (2016). A proof of Onsager's conjecture. <arXiv:1608.08301> - https://arxiv.org/abs/1608.08301
Nash, J. (1954). $C^1$ isometric imbeddings. Annals of Mathematics. Second Series, 60, 383-396 - http://dx.doi.org/10.2307/1969840
Onsager, L. (1949). Statistical hydrodynamics. Nuovo Cimento, 6(Suppl 2), 279-287 - https://doi.org/10.1007/BF02780991

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