Onsager’s Conjecture Almost Everywhere in Time

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Abstract

In recent works by Isett (Hölder continuous Euler flows in three dimensions with compact support in time, pp 1–173, 2012), and later by Buckmaster et al. (Ann Math 2015), iterative schemes were presented for constructing solutions belonging to the Hölder class C1/5-ε of the 3D incompressible Euler equations which do not conserve the total kinetic energy. The cited work is partially motivated by a conjecture of Lars Onsager in 1949 relating to the existence of C1/3-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 C1/3-ε and have compact temporal support.

Original languageEnglish (US)
Pages (from-to)1175-1198
Number of pages24
JournalCommunications In Mathematical Physics
Volume333
Issue number3
DOIs
StatePublished - Jan 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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