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H 1 Multiple traveling waves of the Euler-Korteweg system

Auteurs : Audiard, Corentin (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The Euler-Korteweg system corresponds to compressible, inviscid fluids with capillary forces. It can be used to model diffuse interfaces. Mathematically it reads as the Euler equations with a third order dispersive perturbation corresponding to the capillary tensor.

    In dimension one there exists traveling waves with equal or different limit at infinity, respectively solitons and kinks. Their stability is ruled by a simple criterion a la Grillakis-Shatah-Strauss. This talk is devoted to the construction of multiple traveling waves, namely global solutions that converge as $t\rightarrow \infty $ to a profile made of several (stable) traveling waves. The waves constructed have both solitons and kinks. Multiple traveling waves play a peculiar role in the dynamics of dispersive equations, as they correspond to solutions that follow in some sense a purely nonlinear evolution.

    Keywords : solitons; Euler-Korteweg; stability

    Codes MSC :
    35B35 - Stability of solutions of PDE
    35Q35 - PDEs in connection with fluid mechanics
    35Q53 - KdV-like (Korteweg-de Vries) equations
    35Q31 - Euler equations
    35C07 - Traveling wave solutions of PDE

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 14/10/2019
      Date de captation : 24/09/2019
      Collection : Research talks ; Partial Differential Equations
      Format : MP4
      Durée : 00:43:30
      Domaine : PDE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-09-24_Audiard.mp4

    Informations sur la rencontre

    Nom de la rencontre : Inhomogeneous Flows: Asymptotic Models and Interfaces Evolution / Fluides inhomogènes : modèles asymptotiques et évolution d'interfaces
    Organisateurs de la rencontre : Charve, Frédéric ; Danchin, Raphaël ; Haspot, Boris ; Monniaux, Sylvie
    Dates : 23/09/2019 - 27/09/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1919.html

    Citation Data

    DOI : 10.24350/CIRM.V.19562603
    Cite this video as: Audiard, Corentin (2019). Multiple traveling waves of the Euler-Korteweg system. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19562603
    URI : http://dx.doi.org/10.24350/CIRM.V.19562603

    Voir aussi


    1. C.Audiard, Existence of multi-traveling waves in capillary fluids, to appear Proc.Roy.Soc.Edinburgh. - https://arxiv.org/abs/1809.01454

    2. S.Benzoni, R.Danchin, S.Descombes and D.Jamet, Structure of Korteweg models and stability of diffuse interfaces, Interfaces free bound. 7 (2005), 371–414. - http://dx.doi.org/10.4171/IFB/130

    3. M.Ming, F.Rousset, N.Tzvetkov, Multi-solitons and related solutions for the waterwaves system, SIAM J.Math.Anal. 47 (2015), 897-954 - https://doi.org/10.1137/140960220