2017/10/23 by Benjamin Melinand, Melinand, Benjamin
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #math.AP
paper · pdf · doi:10.48550/arxiv.1710.09717
openalex publication_date 2017/10/25 · arxiv created 2018/11/13 · arxiv updated 2018/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.