Locally dissipative solutions of the Euler equations
[Moved Online] Recent Developments in Fluid Dynamics April 12, 2021 - April 30, 2021
Location: SLMath: Online/Virtual
Euler equations
dissipative solutions
Locally Sissipative Solutions of the Euler Equations.mp4
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.
Locally Sissipative Solutions of the Euler Equations.mp4
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