Strichartz Estimates for Water Waves

TL;DR

This paper establishes dispersive Strichartz estimates for 2D water waves, demonstrating both low-regularity and optimal estimates depending on initial data smoothness, advancing understanding of water wave dynamics.

Contribution

It proves Strichartz estimates with derivative loss at low regularity and optimal estimates for smoother data, improving previous results on water wave dispersive properties.

Findings

Strichartz estimates with derivative loss at low regularity

Optimal Strichartz estimates for smoother initial data

Enhanced understanding of dispersive behavior in water waves

Abstract

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 (? = 0, ? = 0)).