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Weak-Strong Uniqueness for Measure-Valued Solutions

  • Yann Brenier
  • Camillo De LellisEmail author
  • László SzékelyhidiJr.
Article

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.

Keywords

Euler Equation Radon Measure Young Measure Incompressible Euler Equation Commun Math Phys 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Yann Brenier
    • 1
  • Camillo De Lellis
    • 2
    Email author
  • László SzékelyhidiJr.
    • 3
  1. 1.CNRSUniversité de NiceWolfgang DöblinFrance
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland
  3. 3.Hausdorff Center for MathematicsUniversität BonnBonnGermany

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