A Toy Model for Damped Water Waves

2022/03/30 by Gary Moon, Moon, Gary · 1 citation
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2203.16645

openalex publication_date 2022/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a toy model for a damped water waves system in a domain Ω_t ⊂ \mathbbT × ℝ. The toy model is based on the paradifferential water waves equation derived in the work of Alazard-Burq-Zuily. The form of damping we utilize we utilize is a modified sponge layer proposed for the three-dimensional water waves system by Clamond, et. al. We show that, in the case of small Cauchy data, solutions to the toy model exhibit a quadratic lifespan. This is done via proving energy estimates with the energy being constructed from appropriately chosen vector fields.

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