BooksStandalone TitlesCollected Volumepp. 13–29

Continuous dissipative Euler flows and a conjecture of Onsager

  • Camillo De Lellis

    Universität Zürich, Switzerland

  • László Székelyhidi Jr.

    Universität Leipzig, Germany
Continuous dissipative Euler flows and a conjecture of Onsager cover

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Abstract

It is known since the pioneering works of Sche er and Shnirelman that there are nontrivial distributional solutions to the Euler equations which are compactly supported in space and time. Obviously these solutions do not respect the classical conservation law for the total kinetic energy and they are therefore very irregular. In recent joint works we have proved the existence of continuous and even Holder continuous solutions which dissipate the kinetic energy. Our theorem might be regarded as a rst step towards a conjecture of Lars Onsager, which in 1949 asserted the existence of dissipative Hölder solutions for any Hölder exponent smaller than 1/3.