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Journal of the European Mathematical Society


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Volume 16, Issue 7, 2014, pp. 1467–1505
DOI: 10.4171/JEMS/466

Published online: 2014-08-23

Dissipative Euler flows and Onsager's conjecture

Camillo De Lellis[1] and László Székelyhidi Jr.[2]

(1) Universität Zürich, Switzerland
(2) Universität Leipzig, Germany

Building upon the techniques introduced in \cite{DS3}, for any $\theta<\frac{1}{10}$ we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent $\theta$. A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent $\theta<\frac{1}{3}$. Our theorem is the first result in this direction.

Keywords: Euler equations, Onsager’s conjecture, turbulence

De Lellis Camillo, Székelyhidi Jr. László: Dissipative Euler flows and Onsager's conjecture. J. Eur. Math. Soc. 16 (2014), 1467-1505. doi: 10.4171/JEMS/466