1304.1049 (Tristan Buckmaster)

Onsager's conjecture almost everywhere in time    [PDF]

Tristan Buckmaster

In recent work by P. Isett (arXiv:1211.4065), and later by Buckmaster, De Lellis and Sz\'ekelyhidi Jr. (arXiv:1302.2815), iterative schemes where presented for constructing solutions belonging to the H\"older class $C^{1/5-\epsilon}$ of the 3D incompressible Euler equations which do not conserve energy. The cited work is partially motivated by a conjecture of Lars Onsager in 1949 relating to the existence of $C^{1/3-\epsilon}$ solutions to the Euler equations which dissipate energy. In this note we show how the later scheme can be adapted in order to prove the existence of non-trivial H\"older continuous solutions which for almost every time belong to the critical Onsager H\"older regularity $C^{1/3-\epsilon}$ and have compact temporal support. The solutions constructed display characteristics reminiscent to the concept of intermittency found in literature related to highly turbulent flows.

View original: http://arxiv.org/abs/1304.1049