Dissipative Euler flows and Onsager's conjecture

Abstract

Building upon the techniques introduced in [15], for any θ < 1/10 we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent θ. A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent θ < 1/3. Our theorem is the first result in this direction. © European Mathematical Society 2014.