Sharp Strichartz estimates for water waves systems

Quang-Huy Nguyen (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semi-classical Strichartz estimates for gravity-capillary waves; for both 2D and 3D waves. Here, by optimal we mean the gains of regularity obtained for the linearized systems. Our proofs combine the paradifferential reductions of Alazard-Burq-Zuily [1, 3] with a dispersive estimate using a localized wave package type parametrix of Koch-Tataru [19].

Mots clés: water waves; Strichartz estimates; semi-classical Strichartz estimates; quasilinear equations

Domaines: Equations aux dérivées partielles [math.AP]

Quang-Huy Nguyen. Sharp Strichartz estimates for water waves systems. 2015. ⟨hal-01238605⟩