Communications in Mathematical Physics

, Volume 165, Issue 1, pp 207–209 | Cite as

Onsager's conjecture on the energy conservation for solutions of Euler's equation

  • Peter Constantin
  • Weinan E 
  • Edriss S. Titi


We give a simple proof of a result conjectured by Onsager [1] on energy conservation for weak solutions of Euler's equation.


Neural Network Statistical Physic Complex System Weak Solution Nonlinear Dynamics 
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  1. 1.
    Onsager, L.: Statistical Hydrodynamics Nuovo Cimento (Supplemento)6, 279 (1949)Google Scholar
  2. 2.
    Eyink, G.: Energy dissipation without viscosity in ideal hydrodynamics, I and II. Preprint, 1992Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Peter Constantin
    • 1
  • Weinan E 
    • 2
  • Edriss S. Titi
    • 3
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Institute for Advanced StudySchool of MathematicsPrincetonUSA
  3. 3.Department of Mathematics and Mechanical and Aerospace EngineeringUniversity of CaliforniaIrvineUSA

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