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arXiv · 1205.3626

Dissipative Euler Flows and Onsager's Conjecture

Camillo De Lellis·László Székelyhidi Jr
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Abstract

For any \theta<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<1/3. Our theorem is the first result in this direction.

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Camillo De Lellis, László Székelyhidi Jr. 2012-05-16. Dissipative Euler Flows and Onsager's Conjecture. https://arxiv.org/abs/1205.3626

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