Small scale creation in the long time behavior of 2d perfect fluids

The main issue of this note is the study of the long time behavior of 2d perfect fluids on the 2-torus governed by the incompressible Euler equations and the genericity of small scale creation in said limit. Its aim is twofold: first introduce non specialists to some key conjectures in the field today due to Shnirelman, Šverák and Yudovich respectively as well as some results towards those conjectures. Second we present a recent result by the author [19] on the generic character of small creation for the Lagrangian flow which is build upon a pioneering Lyapunov construction due to Shnirelman [20].