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H 1 Relative entropy for the Euler-Korteweg system with non-monotone pressure

Auteurs : Giesselmann, Jan (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In this joint work with Athanasios Tzavaras (KAUST) and Corrado Lattanzio (L’Aquila) we develop a relative entropy framework for Hamiltonian flows that in particular covers the Euler-Korteweg system, a well-known diffuse interface model for compressible multiphase flows. We put a particular emphasis on extending the relative entropy framework to the case of non-monotone pressure laws which make the energy functional non-convex.The relative entropy computation directly implies weak (entropic)-strong uniqueness, but we will also outline how it can be used in other contexts. Firstly, we describe how it can be used to rigorously show that in the large friction limit solutions of Euler-Korteweg converge to solutions of the Cahn-Hilliard equation. Secondly, we explain how the relative entropy can be used for obtaining a posteriori error estimates for numerical approximation schemes.

    Keywords : Euler-Korteweg; relative entropy; weak-strong uniqueness

    Codes MSC :
    76D45 - Capillarity, See also {76B45}
    35Q31 - Euler equations
    76T10 - Liquid-gas two-phase flows, bubbly flows

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 14/10/2019
      Date de captation : 24/09/2019
      Collection : Research talks ; Analysis and its Applications ; Numerical Analysis and Scientific Computing
      Format : MP4
      Durée : 00:48:31
      Domaine : Analysis and its Applications ; Numerical Analysis & Scientific Computing
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-09-24_Giesselmann.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.19562803
    Cite this video as: Giesselmann, Jan (2019). Relative entropy for the Euler-Korteweg system with non-monotone pressure. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19562803
    URI : http://dx.doi.org/10.24350/CIRM.V.19562803

    Voir aussi


    1. J. Giesselmann, A. E. Tzavaras. Stability properties of the Euler-Korteweg system with nonmonotone pressures. Appl. Anal. 96 (2017), no. 9, 1528–1546. - https://doi.org/10.1080/00036811.2016.1276175

    2. J. Giesselmann, C. Lattanzio, A. E. Tzavaras. Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics. Arch. Ration. Mech. Anal. 223 (2017), no. 3, 1427–1484. - https://doi.org/10.1007/s00205-016-1063-2

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