On the wave turbulence theory of 2D gravity waves, II: propagation of randomness

Fuente: arXiv
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Main Authors: Deng, Yu, Ionescu, Alexandru, Pusateri, Fabio
Format: Preprint
Published: 2025
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author Deng, Yu
Ionescu, Alexandru
Pusateri, Fabio
author_facet Deng, Yu
Ionescu, Alexandru
Pusateri, Fabio
contents This is the second part of our work initiating the rigorous study of wave turbulence for water waves equations. We combine energy estimates, normal forms, and probabilistic and combinatorial arguments to complete the construction of long-time solutions with random initial data for the 2d (1d interface) gravity water waves system on large tori. This is the first long-time regularity result for solutions of water waves systems with large energy (but small local energy), which is the correct setup for applications to wave turbulence. Such a result is only possible in the presence of randomness.
format Preprint
id arxiv_https___arxiv_org_abs_2504_14304
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the wave turbulence theory of 2D gravity waves, II: propagation of randomness
Deng, Yu
Ionescu, Alexandru
Pusateri, Fabio
Analysis of PDEs
Mathematical Physics
Probability
This is the second part of our work initiating the rigorous study of wave turbulence for water waves equations. We combine energy estimates, normal forms, and probabilistic and combinatorial arguments to complete the construction of long-time solutions with random initial data for the 2d (1d interface) gravity water waves system on large tori. This is the first long-time regularity result for solutions of water waves systems with large energy (but small local energy), which is the correct setup for applications to wave turbulence. Such a result is only possible in the presence of randomness.
title On the wave turbulence theory of 2D gravity waves, II: propagation of randomness
topic Analysis of PDEs
Mathematical Physics
Probability
url https://arxiv.org/abs/2504.14304