Strichartz estimates for gravity water waves

TL;DR

This paper establishes Strichartz estimates for gravity water waves across various dimensions and bottom configurations, even for rough initial data with limited regularity in velocity derivatives and surface curvature.

Contribution

It introduces Strichartz estimates applicable to gravity water waves with minimal regularity assumptions on initial data and domain geometry.

Findings

Proves Strichartz estimates in arbitrary dimensions.

Handles rough initial data with limited regularity.

Applicable to fluid domains with general bottom topographies.

Abstract

We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled in $L^\infty$-norm, or the initial free surface has a curvature not controlled in $L^2$-norm.