Well-Posedness and Long-Time Dynamics of a Water-Waves Model with Time-Varying Boundary Delay

2024/11/07 by George J. Bautista, Roberto de A. Capistrano–Filho, Bautista, G. +5 · 1 citation
Earth and Planetary Sciences · Mathematics · #Arctic and Antarctic ice dynamics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2411.05191

Abstract

A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem by utilizing Kato's variable norm technique and the Fixed-Point Theorem. More significantly, the energy decay for the linearized problem is demonstrated using the energy method.

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