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Weak-Strong Uniqueness for Measure-Valued Solutions

Brenier, Yann ; De Lellis, Camillo ; Székelyhidi Jr., László

In: Communications in Mathematical Physics, 2011, vol. 305, no. 2, p. 351-361

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    Titre
    • Weak-Strong Uniqueness for Measure-Valued Solutions
    Auteur
    • Brenier, Yann. CNRS, Université de Nice, 2800, Wolfgang Döblin, FR, France
    • De Lellis, Camillo. Institut für Mathematik, Universität Zürich, 8057, Zürich, Switzerland
    • Székelyhidi Jr., László. Hausdorff Center for Mathematics, Universität Bonn, 53115, Bonn, Germany
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Communications in Mathematical Physics, 2011, vol. 305, no. 2, p. 351-361. Springer-Verlag
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:318276
    Summary
    We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by DiPerna and Majda in their landmark paper (Commun Math Phys 108(4):667-689, 1987), where in particular global existence to any L 2 initial data was proven. Whether measure-valued solutions agree with classical solutions if the latter exist has apparently remained open. We also show that DiPerna's measure-valued solutions to systems of conservation laws have the weak-strong uniqueness property