Calculus of Variations and Geometric Measure Theory
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C. De Lellis - L. J. Sz\'ekelyhidi

Dissipative Euler flows and Onsager's conjecture

created by delellis on 02 Jul 2013
modified on 05 May 2014


Accepted paper

Inserted: 2 jul 2013
Last Updated: 5 may 2014

Journal: JEMS
Year: 2012


Building upon the techniques introduced in [1], for any $\theta<\frac{1}{10}$ we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are H\"older-continuous with exponent $\theta$. A famous conjecture of Onsager states the existence of such dissipative solutions with any H\"older exponent $\theta<\frac{1}{3}$. Our theorem is the first result in this direction.


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