Pseudo-local property of gravity water waves system

Quang-Huy Nguyen (1)

1 LMO - Laboratoire de Mathématiques d'Orsay

By proving a weighted contraction estimate 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.

Mots clés: gravity water waves; pseudo-local; spatial decay

Domaines: Equations aux dérivées partielles [math.AP]

Quang-Huy Nguyen. Pseudo-local property of gravity water waves system: Pseudo-local property of gravity water waves. 2015. ⟨hal-01171578v1⟩