Derivation and analysis of a new 2D Green-Naghdi system
Abstract
We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard Green-Naghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green-Naghdi equations. Using this property, we show that the solution of these new equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition. Finally, we prove that the new Green-Naghdi equations conserve the almost irrotationality of the vertically averaged horizontal component of the velocity.
Keywords
Cite
@article{arxiv.1001.2850,
title = {Derivation and analysis of a new 2D Green-Naghdi system},
author = {Samer Israwi},
journal= {arXiv preprint arXiv:1001.2850},
year = {2015}
}