A pseudo-local property of gravity water waves system

Quang-Huy Nguyen

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arXiv · 1507.01331

A pseudo-local property of gravity water waves system

Quang-Huy Nguyen

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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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Quang-Huy Nguyen. 2015-07-06. A pseudo-local property of gravity water waves system. https://arxiv.org/abs/1507.01331

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