Onsager's Conjecture Almost Everywhere in Time

In recent works by Isett (Holder 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 Holder class C (1/5-epsilon) 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 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 Holder continuous solutions which for almost every time belong to the critical Onsager Holder regularity C (1/3-epsilon) and have compact temporal support.