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H 2 The Onsager Theorem

Auteurs : De Lellis, Camillo (Auteur de la Conférence)
CIRM (Editeur )

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energy conservation weak solutions Kolmogorov's theory Onsager's conjecture Scheffer's theorem differential inclusions $h$-principle Borisov-Gromov problem continuous dissipative solutions Onsager critical solutions Daneri-Székelyhidi $h$-principle Isett's proof anomalous dissipation questions of the audience

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 :
76B03 - Existence, uniqueness, and regularity theory
35D30 - Weak solutions of PDE
35Q31 - Euler equations

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 18/05/17
    Date de captation : 10/05/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 01:02:57
    Domaine : PDE ; Mathematical Physics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-05-10_De_Lellis.mp4

Informations sur la rencontre

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

Citation Data

DOI : 10.24350/CIRM.V.19165203
Cite this video as: 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

Bibliographie

  1. Buckmaster, T., De Lellis, C., Székelyhidi, L. Jr., & Vicol, V. (2017). Onsager's conjecture for admissible weak solutions. - https://arxiv.org/abs/1701.08678

  2. 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

  3. Isett, P. (2016). A proof of Onsager's conjecture. - https://arxiv.org/abs/1608.08301

  4. Nash, J. (1954). $C^1$ isometric imbeddings. Annals of Mathematics. Second Series, 60, 383-396 - http://dx.doi.org/10.2307/1969840

  5. Onsager, L. (1949). Statistical hydrodynamics. Nuovo Cimento, 6(Suppl 2), 279-287 - https://doi.org/10.1007/BF02780991



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