Damping for fractional wave equations and applications to water waves

TL;DR

This paper analyzes linear damped water wave models motivated by surface wave simulations, establishing explicit energy decay rates and providing some of the first decay results for these models.

Contribution

It offers the first proven decay of energy for certain linear damped water wave models, with explicit decay rates derived.

Findings

Energy decays exponentially for regular initial data

Explicit decay rates are established

First decay results for these models

Abstract

Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give the explicit decay rates for the energy, but do not address reflection/transmission of waves at the interface of the damping. Still for a subset of the models considered, this represents the first result proving the decay of the energy of the surface wave models.