ICTS:29931

Video URL

The Onsager theorem and beyond (RL1)

The Onsager theorem and beyond (RL1)

(2024). The Onsager theorem and beyond (RL1). SciVideos. https://youtu.be/gp_xK50t0ho

The Onsager theorem and beyond (RL1). SciVideos, Sep. 25, 2024, https://youtu.be/gp_xK50t0ho 

          @misc{ scivideos_ICTS:29931,
            doi = {},
            url = {https://youtu.be/gp_xK50t0ho},
            author = {},
            keywords = {},
            language = {en},
            title = {The Onsager theorem and beyond (RL1)},
            publisher = {},
            year = {2024},
            month = {sep},
            note = {ICTS:29931 see, \url{https://scivideos.org/icts-tifr/29931}}
          }
​Camillo De Lellis
Talk numberICTS:29931
Source RepositoryICTS-TIFR
Source EventDeterministic and Stochastic Analysis of Euler and Navier-Stokes Equations
Collection

Abstract

In 1949 Onsager conjectured the existence of Hoelder continuous solutions of the incompressible Euler equations which do not conserve the kinetic energy. A rigorous proof of his statement has been given by Isett in 2017, crowning a decade of efforts in the subject. Onsager's original statement is however motivated by anomalous dissipation in the Navier-Stokes equations: roughly speaking it would be desirable to show that at least some dissipative Euler flow is the ``vanishing viscosity limit''. In these lectures I will review the basic ideas of the first iteration invented by La'szlo' Sze'kelyhidi Jr. and myself to produce continuous solutions which dissipate the total kinetic energy. I will then review the developments which lead Isett to solve the Onsager conjecture and touch upon the new challenges which lie ahead.