Calculus of Variations and Geometric Measure Theory

C. De Lellis

The Nash-Kuiper Theorem and the Onsager conjecture

created by delellis on 09 Mar 2021


Published Paper

Inserted: 9 mar 2021
Last Updated: 9 mar 2021

Journal: ICCM Not.
Volume: 8
Number: 1
Pages: 17-26
Year: 2020


We give an account of the analogies between the Nash--Kuiper $C^1$ solutions of the isometric embedding problem and the weak solutions of the incompressible Euler equations which violate the energy conservation. Such analogies have lead to the recent resolution of a well-known conjecture of Lars Onsager in the theory of fully developed turbulence.