The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Journal of the European Mathematical Society

Full-Text PDF (287 KB) | Metadata | Table of Contents | JEMS summary
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