Dissipative Euler Flows and Onsager's Conjecture

2012/05/16 by De Lellis, Camillo, Székelyhidi, László · 8 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.3626

Abstract

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.

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