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

Abstract

In this paper we consider the 1D Green-Naghdi system over a nonflat bottom. This system describes the evolution of water waves over an uneven bottom in the shallow water regime in terms of the water depth $h$ and the horizontal velocity $u$. Using a Lagrangian formulation of this system on a Sobolev type diffeomorphism group 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.

References in corpus (1)

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