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Weak-Strong Uniqueness for Measure-Valued Solutions

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Abstract

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.

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Authors and Affiliations

  1. CNRS, Université de Nice, Wolfgang Döblin, FR, 2800, France

    Yann Brenier

  2. Institut für Mathematik, Universität Zürich, 8057, Zürich, Switzerland

    Camillo De Lellis

  3. Hausdorff Center for Mathematics, Universität Bonn, 53115, Bonn, Germany

    László Székelyhidi Jr.

Authors
  1. Yann Brenier
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  2. Camillo De Lellis
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  3. László Székelyhidi Jr.
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Correspondence to Camillo De Lellis.

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Communicated by P. Constantin

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Brenier, Y., De Lellis, C. & Székelyhidi, L. Weak-Strong Uniqueness for Measure-Valued Solutions. Commun. Math. Phys. 305, 351–361 (2011). https://doi.org/10.1007/s00220-011-1267-0

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  • DOI: https://doi.org/10.1007/s00220-011-1267-0

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