Small scale creation in the long time behavior of 2d perfect fluids
Ayman Rimah Said1
1 Laboratoire de Mathématiques de Reims (LMR - UMR 9008), U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse - BP 1039, 51687 REIMS cedex 2
Séminaire Laurent Schwartz — EDP et applications (2024-2025), Talk no. 4, 8 p.

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].

Published online:
DOI: 10.5802/slsedp.174
Ayman Rimah Said 1

1 Laboratoire de Mathématiques de Reims (LMR - UMR 9008), U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse - BP 1039, 51687 REIMS cedex 2 
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Ayman Rimah Said. Small scale creation in the long time behavior of 2d perfect fluids. Séminaire Laurent Schwartz — EDP et applications (2024-2025), Talk no. 4, 8 p. doi : 10.5802/slsedp.174. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.174/

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