DISSIPATIVE EULER FLOWS AND ONSAGER’S CONJECTURE

Abstract

Building upon the techniques introduced in [15], 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.