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

2014/02/13 by Ronan Monjarret, Monjarret, Ronan
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #15A15 #15A18 #35A07 #35L45 #35P15 #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #math-ph #math.AP #math.MP #msc:15A15 #msc:15A18 #msc:35A07 #msc:35L45 #msc:35P15

paper · pdf · doi:10.48550/arxiv.1402.3194

20 pages, 1 figure

arxiv created 2014/02/13 · openalex publication_date 2014/02/13 · arxiv updated 2014/11/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we adress the question of the hyperbolicity and the local well-posedness of the two-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 weak density-stratification assumption. Finally, we consider a new conservative two-layer shallow water model, prove the hyperbolicity and the local well-posedness and rely it to the basic two-layer shallow water model.

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