Onsager's conjecture almost everywhere in time

2013/04/03 by Buckmaster, Tristan · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1304.1049

Abstract

In recent work by Isett (arXiv:1211.4065), and later by Buckmaster, De Lellis, Isett and Székelyhidi Jr. (arXiv:1302.2815), iterative schemes where presented for constructing solutions belonging to the Hölder class C^1/5-ε 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-ε 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 Hölder continuous solutions which for almost every time belong to the critical Onsager Hölder regularity C^1/3-ε and have compact temporal support.

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