43 citations · 378 across the 28 of their papers we have counts for
4 papers · 1 filter
A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part II: Justification as a shallow water approximation
Vincent Duchêne, Tatsuo Iguchi
We consider the Kakinuma model for the motion of interfacial gravity waves. The Kakinuma model is a system of Euler-Lagrange equations for an approximate Lagrangian, which is obtai…
On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity
Vincent Duchêne, Roberta Bianchini
This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of…
Many Models for Water Waves
Vincent Duchêne
This document is an announcement and preview of a memoir whose full version is available on the Open Math Notes repository of the American Mathematical Society (OMN:202109.111309).…
Rectification of a deep water model for surface gravity waves
Vincent Duchêne, Benjamin Melinand
In this work we discuss an approximate model for the propagation of deep irrotational water waves, specifically the model obtained by keeping only quadratic nonlinearities in the w…