Anomalous dissipation for $1/5$-Hölder Euler flows

created by delellis on 02 Sep 2014
modified by paolini on 16 Sep 2014

[BibTeX]

Accepted Paper

Inserted: 2 sep 2014
Last Updated: 16 sep 2014

Journal: Ann. of Math.
Year: 2014
In a recent paper the third author has improved upon the methods, introducing some novel ideas on how to deal with this obstruction, thereby reaching a better Hölder exponent -- albeit below the one conjectured by Onsager. In this paper we give a shorter proof of this final result, adhering more to the original scheme of the second and fourth author and introducing some new devices. More precisely we show that for any positive $\varepsilon$ there exist periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy and belong to the Hölder class $C^{1/5-\varepsilon}$.