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

Hasan Inci

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arXiv · 2111.06192

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

Hasan Inci

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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 $(1+H^s(\R)) \times H^{s+1}(\R),\; s > 1/2$. This improves the local well-posedness range for the 1D Green-Naghdi system.

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Hasan Inci. 2021-11-11. On a Lagrangian formulation of the 1D Green-Naghdi system. https://arxiv.org/abs/2111.06192

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