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  • Séminaire Laurent Schwartz — EDP et applications
  • Year 2024-2025
  • Talk no. 4
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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.
  • Abstract

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].

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Published online: 2025-02-17
DOI: 10.5802/slsedp.174
Author's affiliations:
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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@article{SLSEDP_2024-2025____A1_0,
     author = {Ayman Rimah Said},
     title = {Small scale creation in the long time behavior of 2d~perfect~fluids},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:4},
     pages = {1--8},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2024-2025},
     doi = {10.5802/slsedp.174},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.174/}
}
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TI  - Small scale creation in the long time behavior of 2d perfect fluids
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:4
PY  - 2024-2025
SP  - 1
EP  - 8
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.174/
DO  - 10.5802/slsedp.174
LA  - en
ID  - SLSEDP_2024-2025____A1_0
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%0 Journal Article
%A Ayman Rimah Said
%T Small scale creation in the long time behavior of 2d perfect fluids
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:4
%D 2024-2025
%P 1-8
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
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%R 10.5802/slsedp.174
%G en
%F SLSEDP_2024-2025____A1_0
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/
  • References
  • Cited by

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