Work

Decorated trees, arborification for cancellations in wave turbulence

Year: 2025

Type: article

Abstract: 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.

Source: Séminaire Laurent Schwartz — EDP et applications

DOI: 10.5802/slsedp.180

Author: Yvain Bruned

Institutions: Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine, Centre de Mathématiques Laurent Schwartz, Université de Lorraine

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, HORIZON EUROPE European Research Council

Award: Low Regularity Dynamics via Decorated Trees