On a Lagrangian formulation of the 1D Green-Naghdi system

Abstract

In this paper we consider the 1D Green-Naghdi system. This system describes the evolution of water waves over a flat bottom in the shallow water regime in terms of the surface height $h$ and the horizontal velocity $u$. We give a Lagrangian formulation of the 1D Green-Naghdi system on a Sobolev type diffeomorphism group. As an application of this formulation we prove local well-posedness for $(h,u)$ in the Sobolev space $(1+H^s(\mathbb{R}))\times H^{s+1}(\mathbb{R}),s>1/2$. This improves the local well-posedness range for the 1D Green-Naghdi system.

Cited by in corpus (1)

• On the local well-posedness of the 1D Green-Naghdi system over a nonflat bottom