Sharp Strichartz estimates for water waves systems

Quang-Huy Nguyen

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arXiv · 1512.02359

Sharp Strichartz estimates for water waves systems

Quang-Huy Nguyen

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Abstract

Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, 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 (over the Sobolev embedding from Sobolev spaces to Hölder spaces) obtained for the linearized systems. Our proofs combine the paradifferential reductions of Alazard-Burq-Zuily with a dispersive estimate using a localized wave package type parametrix of Koch-Tataru.

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Quang-Huy Nguyen. 2016-09-26. Sharp Strichartz estimates for water waves systems. https://arxiv.org/abs/1512.02359

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