English
The Onsager Theorem
Post-edited
Auteurs : De Lellis, Camillo (Auteur de la Conférence)
CIRM (Editeur )
76B03 - Existence, uniqueness, and regularity theory
35D30 - Weak solutions of PDE
35Q31 - Euler equations
CIRM (Editeur )
Résumé :
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.
Codes MSC : 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.
76B03 - Existence, uniqueness, and regularity theory
35D30 - Weak solutions of PDE
35Q31 - Euler equations
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 18/05/17 Date de captation : 10/05/17 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Durée : 01:02:57 Audience : Researchers Download : https://videos.cirm-math.fr/2017-05-10_De_Lellis.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Vorticity, rotation and symmetry (IV): Complex fluids and the issue of regularity / Vorticité, rotation et symétrie (IV) : fluides complexes et problèmes de régularitéOrganisateurs de la rencontre : Danchin, Raphaël ; Farwig, Reinhard ; Neustupa, Jiri ; Penel, Patrick Dates : 08/05/17 - 12/05/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1588.html
Données de citation
DOI : 10.24350/CIRM.V.19165203Citer cette vidéo: De Lellis, Camillo (2017). The Onsager Theorem. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19165203 URI : http://dx.doi.org/10.24350/CIRM.V.19165203 |
Voir aussi
- [Multi angle] $L^q$-$L^r$ estimates of a generalized Oseen evolution operator, with applications to the Navier-Stokes flow past a rotating obstacle / Auteur de la Conférence Hishida, Toshiaki.
- [Multi angle] Large time behavior of solutions to 3-D MHD system with initial data near equilibrium / Auteur de la Conférence Zhang, Ping.
- [Multi angle] An asymptotic regime for the Vlasov-Poisson system / Auteur de la Conférence Miot, Evelyne.
- [Multi angle] On the analysis of a class of thermodynamically compatible viscoelastic fluids with stress diffusion / Auteur de la Conférence Málek, Josef.
Bibliographie
- Buckmaster, T., De Lellis, C., Székelyhidi, L. Jr., & Vicol, V. (2017). Onsager's conjecture for admissible weak solutions.
- 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.
- 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
