arXiv 1507.013312015-07math.AP

A pseudo-local property of gravity water waves system

Quang-Huy Nguyen

备注：: We improved the main results and the paradifferential calculus for a general class of weights. Typos fixed, explanations and details added

英文摘要：

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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