Calculus of Variations and Geometric Measure Theory

C. De Lellis - L. J. László Jr Székelyhidi

Dissipative Euler flows and Onsager's conjecture

created by delellis on 02 Jul 2013
modified on 24 May 2017


Published Paper

Inserted: 2 jul 2013
Last Updated: 24 may 2017

Journal: J. Eur. Math. Soc. (JEMS)
Volume: 16
Pages: 1467–1505
Year: 2014


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.