A pseudo-local property of gravity water waves system
Analysis of PDEs
2016-03-15 v2
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.
Cite
@article{arxiv.1507.01331,
title = {A pseudo-local property of gravity water waves system},
author = {Quang-Huy Nguyen},
journal= {arXiv preprint arXiv:1507.01331},
year = {2016}
}
Comments
We improved the main results and the paradifferential calculus for a general class of weights. Typos fixed, explanations and details added