# Dissipative Euler flows and Onsager's conjecture

### Camillo De Lellis

Universität Zürich, Switzerland### László Székelyhidi Jr.

Universität Leipzig, Germany

## Abstract

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.

## Cite this article

Camillo De Lellis, László Székelyhidi Jr., Dissipative Euler flows and Onsager's conjecture. J. Eur. Math. Soc. 16 (2014), no. 7, pp. 1467–1505

DOI 10.4171/JEMS/466