In this work, we review part of the results obtained in [12] for computing cancellations for dispersive PDEs with random initial data. The idea is to get a new combinatorial perspective on the cancellations discovered by Deng and Hani (see [16]) in the context of Wave Turbulence when one wants to derive rigorously wave-kinetic equations. This new perspective is based on decorated trees developed for low regularity schemes, together with a well-chosen arborification map that rewrites these trees into linear combinations of words. With this new combinatorial basis, one develops graphical rules to compute cancellations.
@article{SLSEDP_2024-2025____A7_0,
author = {Yvain Bruned},
title = {Decorated trees, arborification for cancellations in wave~turbulence},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:16},
pages = {1--15},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2024-2025},
doi = {10.5802/slsedp.180},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.180/}
}
TY - JOUR AU - Yvain Bruned TI - Decorated trees, arborification for cancellations in wave turbulence JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:16 PY - 2024-2025 SP - 1 EP - 15 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.180/ DO - 10.5802/slsedp.180 LA - en ID - SLSEDP_2024-2025____A7_0 ER -
%0 Journal Article %A Yvain Bruned %T Decorated trees, arborification for cancellations in wave turbulence %J Séminaire Laurent Schwartz — EDP et applications %Z talk:16 %D 2024-2025 %P 1-15 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.180/ %R 10.5802/slsedp.180 %G en %F SLSEDP_2024-2025____A7_0
Yvain Bruned. Decorated trees, arborification for cancellations in wave turbulence. Séminaire Laurent Schwartz — EDP et applications (2024-2025), Exposé no. 16, 15 p. doi : 10.5802/slsedp.180. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.180/
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