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Locally dissipative solutions of the Euler equations

[Moved Online] Recent Developments in Fluid Dynamics April 12, 2021 - April 30, 2021

April 23, 2021 (08:00 AM PDT - 08:50 AM PDT)
Speaker(s): Camillo De Lellis (Institute for Advanced Study)
Location: SLMath: Online/Virtual
Tags/Keywords
  • Euler equations

  • dissipative solutions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Locally Sissipative Solutions of the Euler Equations.mp4

Abstract

The Onsager conjecture, recently solved by Phil Isett, states that, below a certain threshold regularity, Hoelder continuous solutions of the Euler equations might dissipate the kinetic energy. The original work of Onsager was motivated by the phenomenon of anomalous dissipation and a rigorous mathematical justification of the latter should show that the energy dissipation in the Navier-Stokes equations is, in a suitable statistical sense, independent of the viscosity. In particular it makes much more sense to look for solutions of the Euler equations which, besides dissipating the {\em total} kinetic energy, satisfy as well a suitable form of local energy inequality. Such solutions were first shown to exist by Laszlo Szekelyhidi Jr. and myself. In this talk I will review the methods used so far to approach their existence and the most recent results by Isett and by Hyunju Kwon and myself.

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Video/Audio Files

Locally Sissipative Solutions of the Euler Equations.mp4

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