A pseudo-local property of gravity water waves system

2015/07/06 by Quang-Huy Nguyen, Nguyen, Quang-Huy
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · doi:10.48550/arxiv.1507.01331

openalex publication_date 2015/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By proving a weighted contraction estimate in uniformly local Sobolev spaces for the flow of gravity water waves, we show that this nonlocal system is in fact pseudo-local in the following sense: locally in time, the dynamic far away from a given bounded region has a small effect on that region (again, in a sense that we will make precise in the article). Our estimate on the flow also implies a new spatial decay property of the waves. To prove this result, we establish a paradifferential calculus theory in uniformly local Sobolev spaces with weights.

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