Local Well-Posedness of the Gravity-Capillary Water Waves System in the Presence of Geometry and Damping

Autor:	Moon, Gary
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs 76B03 76B15 76B45 35Q31 35Q35
Druh dokumentu:	Working Paper
Popis:	We consider the gravity-capillary water waves problem in a domain $\Omega_t \subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features. Namely, we consider a variable bottom, smooth obstacles in the flow and a constant background current. We utilize a vortex sheet model introduced by Ambrose, et. al. in arXiv:2108.01786. We show that the water waves problem is locally-in-time well-posed in this geometric setting and study the lifespan of solutions. We then add a damping term and derive evolution equations that account for the damper. Ultimately, we show that the same well-posedness and lifespan results apply to the damped system. We primarily utilize energy methods. Comment: Fixed typos and improved presentation. Edited references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.04713 Zobrazit plný text záznamu View this record from Arxiv