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H 1 The H-Principle and Turbulence

Auteurs : Székelyhidi, László (Auteur de la Conférence)
... (Editeur )

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    Résumé : It is well known since the pioneering work of Scheffer and Shnirelman that weak solutions of the incompressible Euler equations exhibit a wild behaviour, which is very different from that of classical solutions. Nevertheless, weak solutions in three space dimensions have been studied in connection with a long-standing conjecture of Lars Onsager from 1949 concerning anomalous dissipation and, more generally, because of their possible relevance to the K41 theory of turbulence.
    In recent joint work with Camillo De Lellis we established a connection between the theory of weak solutions of the Euler equations and the Nash-Kuiper theorem on rough isometric immersions. Through this connection we interpret the wild behaviour of weak solutions of Euler as an instance of Gromov's h-principle.
    In this lecture we explain this connection and outline recent progress towards Onsager's conjecture.

    Codes MSC :
    76B03 - Existence, uniqueness, and regularity theory
    35Q31 - Euler equations

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 25/08/14
      Date de captation : 07/05/14
      Collection : Research talks ; Partial Differential Equations ; Mathematical Physics
      Format : MP4
      Durée : 00:46:02
      Domaine : PDE ; Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-05-07_Szekelyhidi.mp4

    Informations sur la rencontre

    Nom de la rencontre : Vorticity, rotation and symmetry (III) - approaching limiting cases of fluid flows / Vorticité, rotation et symétrie (III) - analyse des situations limites en théorie des fluides
    Organisateurs de la rencontre : Farwig, Reinhard ; Neustupa, Jiri ; Penel, Patrick
    Dates : 05/05/14 - 09/05/14
    Année de la rencontre : 2014
    URL Congrès : https://www.cirm-math.fr/Archives/?EX=in...

    Citation Data

    DOI : 10.24350/CIRM.V.19028203
    Cite this video as: Székelyhidi, László (2014). The H-Principle and Turbulence. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19028203
    URI : http://dx.doi.org/10.24350/CIRM.V.19028203


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