2021/02/16 by Bashar Bhorbatly, Ralph Lteif, Bhorbatly, Bashar +4
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing
paper · doi:10.48550/arxiv.2102.08045
openalex publication_date 2021/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This study deals with higher-ordered asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and uniqueness of solution on a relevant time scale of order 1/√(\eps) and showing that the solution's behavior is close to the solution of the water waves equations with a better precision corresponding to initial data, the asymptotic model is well-posed in the sense of Hadamard. Then we compared several water waves solitary solutions with respect to the numerical solution of our model. At last, we solve explicitly this model and validate the results numerically.