A Morawetz inequality for water waves

TL;DR

This paper establishes a Morawetz inequality for 2D gravity water waves, providing uniform local energy decay estimates over time, applicable to both finite and infinite depth scenarios.

Contribution

It introduces a Morawetz inequality for water waves that holds uniformly in the infinite depth limit, advancing understanding of energy decay in fluid dynamics.

Findings

Proves local energy decay estimates for water waves

Establishes uniform bounds in the infinite depth limit

Extends Morawetz inequalities to gravity water waves

Abstract

We consider gravity water waves in two space dimensions, with finite or infinite depth. Assuming some uniform scale invariant Sobolev bounds for the solutions, we prove local energy decay (Morawetz) estimates globally in time. Our result is uniform in the infinite depth limit.