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Strichartz estimates for water waves

Thomas AlazardNicolas BurqClaude Zuily — 2011

Annales scientifiques de l'École Normale Supérieure

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system with surface tension. 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 [3]. 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 )).

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