Energy conservation and Onsager's conjecture for the Euler equations
| dc.creator | Cheskidov, A. | |
| dc.creator | Constantin, P. | |
| dc.creator | Friedlander, S. | |
| dc.creator | Shvydkoy, R. | |
| dc.date | 2007-04-05 | |
| dc.date.accessioned | 2026-07-07T07:55:21Z | |
| dc.date.available | 2026-07-07T07:55:21Z | |
| dc.description | Onsager conjectured that weak solutions of the Euler equations for incompressible fluids in 3D conserve energy only if they have a certain minimal smoothness, (of order of 1/3 fractional derivatives) and that they dissipate energy if they are rougher. In this paper we prove that energy is conserved for velocities in the function space $B^{1/3}_{3,c(\NN)}$. We show that this space is sharp in a natural sense. We phrase the energy spectrum in terms of the Littlewood-Paley decomposition and show that the energy flux is controlled by local interactions. This locality is shown to hold also for the helicity flux; moreover, every weak solution of the Euler equations that belongs to $B^{2/3}_{3,c(\NN)}$ conserves helicity. In contrast, in two dimensions, the strong locality of the enstrophy holds only in the ultraviolet range. | |
| dc.identifier | https://arxiv.org/abs/0704.0759 | |
| dc.identifier | http://arxiv.org/abs/0704.0759 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126939 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 76B03, 76F02 | |
| dc.title | Energy conservation and Onsager's conjecture for the Euler equations | |
| dc.type | text |