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H 2 Various aspects of the dynamics of the cubic Szegö solutions

Auteurs : Grellier, Sandrine (Auteur de la Conférence)
CIRM (Editeur )

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arbitrarily large finite growth for cubic NLS cubic Szegö equation Szegö dynamics two Lax pairs action-angle variables wave turbulence phenomenon uniformly bounded trajectories questions of the audience

Résumé : The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform analyticity for a large set of initial data, turbulence phenomenon for a dense set of smooth initial data in large Sobolev spaces.
From joint works with Patrick Gérard.

Codes MSC :
35B15 - Almost and pseudo-almost periodic solutions of PDE
35B40 - Asymptotic behavior of solutions of PDE
35Q55 - NLS-like equations (nonlinear Schrödinger)
37K15 - Integration of completely integrable systems by inverse spectral and scattering methods
47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 13/07/17
    Date de captation : 05/07/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:56:37
    Domaine : PDE ; Dynamical Systems & ODE
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-07-04_Grellier.mp4

Informations sur la rencontre

Nom du congrès : Asymptotic analysis of evolution equations / Analyse asymptotique des équations d'évolution
Organisteurs Congrès : Burq, Nicolas ; Delort, Jean-Marc ; Gérard, Patrick ; Koch, Herbert ; Thomann, Laurent
Dates : 03/07/17 - 07/07/17
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1546.html

Citation Data

DOI : 10.24350/CIRM.V.19192503
Cite this video as: Grellier, Sandrine (2017). Various aspects of the dynamics of the cubic Szegö solutions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19192503
URI : http://dx.doi.org/10.24350/CIRM.V.19192503

Voir aussi

Bibliographie

  1. Gérard, P., & Grellier, S. (2017). The cubic Szegö equation and Hankel operators. Astérisque 389. Paris: Société Mathématique de France - http://smf4.emath.fr/Publications//Asterisque/2017/389/pdf/smf_ast_389.pdf

  2. Gérard, P., & Grellier, S. (2016). On the growth of Sobolev norms for the cubic Szegö equation. Séminaire Laurent Schwartz. EDP et Applications 2014-2015, Exp. No. 11 - http://dx.doi.org/10.5802/slsedp.70



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