Dissipative Euler Flows and Onsager's Conjecture
Abstract
For any θ<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 θ. A famous conjecture of Onsager states the existence of such dissipative solutions with any H\"older exponent θ<1/3. Our theorem is the first result in this direction.
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