STRICHARTZ ESTIMATES FOR WATER WAVES

Thomas Alazard (1) , Nicolas Burq (1) , Claude Zuily (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [2]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at (η = 0, ψ = 0)).

Domaines: Equations aux dérivées partielles [math.AP]

Thomas Alazard, Nicolas Burq, Claude Zuily. STRICHARTZ ESTIMATES FOR WATER WAVES. 2010. ⟨hal-00452071⟩