English

Onsager's conjecture almost everywhere in time

Analysis of PDEs 2014-10-09 v4 Mathematical Physics math.MP

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 C1/5ϵC^{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 C1/3ϵC^{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 C1/3ϵC^{1/3-\epsilon} 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

R2 v1 2026-06-21T23:53:15.668Z