Full justification of a new Green-Naghdi system for internal waves propagation over large topography variation

Abstract

We consider here asymptotic models describing the evolution of internal waves propagating between a flat rigid-lid and a variable topography. In this paper, we derive and fully justify (in the sense of consistency, well-posedness and convergence) a new Green-Naghdi model in the Camassa-Holm regime taking into account large amplitude topography variations, thus relaxing the smallness assumption on the topographic variation parameter used in [Communications on Pure & Applied Analysis, 2015, 14 (6): 2203-2230] and hence improving the result of the aforementioned paper.Comment: arXiv admin note: text overlap with arXiv:1412.398