Weak-Strong Uniqueness for Measure-Valued Solutions

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


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.


Euler Equation Radon Measure Young Measure Incompressible Euler Equation Commun Math Phys 
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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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