Local well-posedness of the multi-layer shallow-water model with free surface

2014/11/10 by Ronan Monjarret, Monjarret, Ronan
Earth and Planetary Sciences · Mathematics · #15A15 #15A18 #35A07 #35L45 #35P15 #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #math.AP #msc:15A15 #msc:15A18 #msc:35A07 #msc:35L45 #msc:35P15

paper · pdf · doi:10.48550/arxiv.1411.2342

55 pages, 2 figures, Ph.D. work

openalex publication_date 2014/11/10 · arxiv created 2014/11/29 · arxiv updated 2014/12/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we address the question of the hyperbolicity and the local well- posedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in H^s(R²), with s > 2. Then, we analyze rigorously the eigenstructure associated to this model and prove a more general criterion of hyperbolicity and local well-posedness, under a particular asymptotic regime and a weak stratification assumptions of the densities and the velocities. Finally, we consider a new conservative multi-layer shallow water model, we prove the symmetrizability, the hyperbolicity and the local well-posedness and rely it to the basic multi-layer shallow water model.

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