JournalsjemsVol. 16, No. 7pp. 1467–1505

Dissipative Euler flows and Onsager's conjecture

  • Camillo De Lellis

    Universität Zürich, Switzerland
  • László Székelyhidi Jr.

    Universität Leipzig, Germany
Dissipative Euler flows and Onsager's conjecture cover
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Abstract

Building upon the techniques introduced in \cite{DS3}, for any θ<110\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 θ\theta. A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent θ<13\theta<\frac{1}{3}. Our theorem is the first result in this direction.

Cite this article

Camillo De Lellis, László Székelyhidi Jr., Dissipative Euler flows and Onsager's conjecture. J. Eur. Math. Soc. 16 (2014), no. 7, pp. 1467–1505

DOI 10.4171/JEMS/466