Inventiones mathematicae

, Volume 193, Issue 2, pp 377–407 | Cite as

Dissipative continuous Euler flows

  • Camillo De LellisEmail author
  • László SzékelyhidiJr.


We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.


Euler Equation Reynolds Stress Continuous Solution Total Kinetic Energy Isometric Embedding 
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We wish to thank Peter Constantin and Sergio Conti for several very valuable discussions on earlier attempts to prove Theorem 1.1. Moreover we are grateful to Antoine Choffrut for several comments on earlier versions of the paper, which considerably improved its readability. The first author acknowledges the support of the SFB Grant TR71, the second author acknowledges the support of the ERC Grant Agreement No. 277993 and the support of the Hausdorff Center for Mathematics in Bonn.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Institut für MathematikUniversität LeipzigLeipzigGermany

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