Onsager conjecture, the Kolmogorov 1/3 law and the 1984 Kato criteria in bounded domains with boundaries
Mardi à 17h00 en Amphi S3 043.
Claude Bardos (LJLL, Paris 6)
In this talk I will recall the Onsager conjecture and compare it to the issue of anomalous energy dissipation and to the Kolmogorov 1/3 law . Then I will give a proof of the local conservation of energy under convenient hypothesis in a domain with boundary and show how this implies the absence of anomalous energy dissipation. Eventually I will give several forms of a basic theorem of Kato in the presence of a Lipschitz solution of the Euler equations. Insisting that in such case the absence of anomalous energy dissipation is equivalent to the persistence of regularity in the zero viscosity limit.
This is a report on a joint work with E. Titi and E. Wiedemann.