Well-posedness of the Green-Naghdi and Boussinesq-Peregrine systems

Abstract

In this paper we address the Cauchy problem for two systems modeling the propagation of long gravity waves in a layer of homogeneous, incompressible and inviscid fluid delimited above by a free surface, and below by a non-necessarily flat rigid bottom. Concerning the Green-Naghdi system, we improve the result of Alvarez-Samaniego and Lannes (Invent. Math., 2008) in the sense that much less regular data are allowed, and no loss of derivatives is involved. Concerning the Boussinesq-Peregrine system, we improve the lower bound on the time of existence provided by M{é}sognon-Gireau (Adv. Differential Equations, 2017). The main ingredient is a physically motivated change of unknowns revealing the quasilinear structure of the systems, from which energy methods are implemented.

In v2: Appendix A added, and slight modifications in the introduction

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Cited by in corpus (7)

• Modeling shallow water waves
• Rigorous justification of the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi model
• Boussinesq-Peregrine water wave models and their numerical approximation
• A regularized shallow-water waves system with slip-wall boundary conditions in a basin: Theory and numerical analysis
• Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart
• Rigid Lid limit in shallow water over a flat bottom
• Helicity in dispersive fluid mechanics