Onsager's conjecture almost everywhere in time
Abstract
In recent work by Isett (arXiv:1211.4065), and later by Buckmaster, De Lellis, Isett and Sz\'ekelyhidi Jr. (arXiv:1302.2815), iterative schemes where presented for constructing solutions belonging to the H\"older class 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 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 and have compact temporal support.
Keywords
Cite
@article{arxiv.1304.1049,
title = {Onsager's conjecture almost everywhere in time},
author = {Tristan Buckmaster},
journal= {arXiv preprint arXiv:1304.1049},
year = {2014}
}
Comments
26 pages, minor fixes, updated references, minor clean up