Helena Nussenzveig Lopes
Federal University of Rio de Janeiro
Title
Beyond the resolution of the Onsager Conjecture
Abstract
In a seminal 1949 paper Lars Onsager conjectured, using dimensional analysis, that it might be possible for some incompressible inviscid flows not to conserve energy, as long as they were sufficiently rough. This is in line with the Kolmogorov 1941 theory of turbulence. More precisely, Onsager conjectured that, if a solution of the Euler equations were more regular than Holder continuous with exponent 1/3 then energy would be conserved; otherwise energy might not be balanced. Research on the Onsager Conjecture developed intensely in the early 2000s, following DeLellis and Sezekelyhidi's introduction of the use of convex integration to fluid dynamics. The Conjecture was fully resolved by Isett in 2018 but there are still many issues to be understood. In this talk I will give a brief account of the resolution of the Onsager Conjecture and then concentrate on ongoing subsequent research, particularly regarding two dimensional flows. I aim to discuss recent results for vanishing viscosity solutions in the supercritical case.