Relative entropy for the Euler-Korteweg system with non-monotone pressure | Vidéo | Carmin.tv

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

By Jan Giesselmann

Appears in collection : Inhomogeneous Flows: Asymptotic Models and Interfaces Evolution / Fluides inhomogènes : modèles asymptotiques et évolution d'interfaces

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.

Information about the video

Date of recording 24/09/2019
Date of publication 14/10/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19562803
Cite this video Giesselmann, Jan (24/09/2019). Relative entropy for the Euler-Korteweg system with non-monotone pressure. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19562803
URL https://dx.doi.org/10.24350/CIRM.V.19562803

Domain(s)

Analysis of PDEs

Bibliography

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
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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