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Statistical Solutions of the 2D Euler Equations

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TURW02 - Rigorous analysis of incompressible fluid models and turbulence

It has been well-accepted for a long time that turbulence requires a probabilistic description. Accordingly, concepts of statistical solution for the Navier-Stokes equations were introduced by Foias and Vishik-Fursikov in the 1970s. In contrast, similar notions for the Euler equations have received comparatively little attention. We show how the deterministic existence theory for the 2D Euler equations with unbounded vorticity (even in the Delort class) can be established in the statistical context, and discuss the relation with the measure-valued solutions of DiPerna-Majda and the Young measure-based statistical solution concept of Fjordholm-Lanthaler-Mishra. This is joint work with Raphael Wagner. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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