The KP approximation under a weak Coriolis forcing
Analysis of PDEs
2018-11-14 v3
Abstract
In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.
Keywords
Cite
@article{arxiv.1710.09717,
title = {The KP approximation under a weak Coriolis forcing},
author = {Benjamin Melinand},
journal= {arXiv preprint arXiv:1710.09717},
year = {2018}
}