43 citations · 378 across the 28 of their papers we have counts for
29 papers
Three-scale singular limits with applications to rapidly rotating fluids and the hyperbolization of dispersive systems
Vincent Duchêne, Arnaud Duran, Khawla Msheik
We consider singular problems for a general class of quasilinear hyperbolic systems that involve two a priori independent stiff parameters. We argue that such situations may lead t…
The Fourier spectral approach to the spatial discretization of quasilinear hyperbolic systems
Vincent Duchêne, Johanna Ulvedal Marstrander
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability…
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…
A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness
Vincent Duchêne, Tatsuo Iguchi
We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well-known, the full model for interfacial gravity waves has a variational structure wh…
Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart
Vincent Duchêne, Christian Klein
We perform numerical experiments on the Serre-Green-Naghdi (SGN) equations and a fully dispersive "Whitham-Green-Naghdi" (WGN) counterpart in dimension 1. In particular, solitary w…
A Hamiltonian structure of the Isobe-Kakinuma model for water waves
Vincent Duchêne, Tatsuo Iguchi
We consider the Isobe-Kakinuma model for water waves, which is obtained as the system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves.…
Large-time asymptotic stability of Riemann shocks of scalar balance laws
Vincent Duchêne, Luis Miguel Rodrigues
We prove the large-time asymptotic orbital stability of strictly entropic Riemann shock solutions of first order scalar hyperbolic balance laws, under piecewise regular perturbatio…
Rigorous justification of the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi model
Vincent Duchêne
The (Serre-)Green-Naghdi system is a non-hydrostatic model for the propagation of surface gravity waves in the shallow-water regime. Recently , Favrie and Gavrilyuk proposed in [No…
Solitary wave solutions to a class of modified Green-Naghdi systems
Vincent Duchêne, Dag Nilsson, Erik Wahlén
We provide the existence and asymptotic description of solitary wave solutions to a class of modified Green-Naghdi systems, modeling the propagation of long surface or internal wav…
Well-posedness of the Green-Naghdi and Boussinesq-Peregrine systems
Vincent Duchêne, Samer Israwi
In this paper we address the Cauchy problem for two systems modeling the propagation of long gravity waves in a layer of homogeneous, incompressible and inviscid fluid delimited ab…
Spectral asymptotics for the Schrödinger operator on the line with spreading and oscillating potentials
Vincent Duchêne, Nicolas Raymond
This study is devoted to the asymptotic spectral analysis of multiscale Schrödinger operators with oscillating and decaying electric potentials. Different regimes, related to scali…
The multilayer shallow water system in the limit of small density contrast
Vincent Duchêne
We study the inviscid multilayer Saint-Venant (or shallow-water) system in the limit of small density contrast. We show that, under reasonable hyperbolicity conditions on the flow…
A new class of two-layer Green-Naghdi systems with improved frequency dispersion
Vincent Duchêne, Samer Israwi, Raafat Talhouk
We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1+1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, i…
Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes
Vincent Duchêne, Iva Vukićević, Michael I. Weinstein
Let denote a periodic function on the real line. The Schrödinger operator, , has spectrum equal to the union of closed real interv…
Spectral asymptotics of a broken delta interaction
Vincent Duchene, Nicolas Raymond
This paper is concerned with the spectral analysis of a Hamiltonian with a -interaction supported along a broken line with angle . The bound states with energy slightly below…
On the rigid-lid approximation for two shallow layers of immiscible fluids with small density contrast
Vincent Duchene
The rigid-lid approximation is a commonly used simplification in the study of density-stratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the…
Shallow water asymptotic models for the propagation of internal waves
Vincent Duchene, Samer Israwi, Raafat Talhouk
We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We rev…
A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regime
Vincent Duchene, Samer Israwi, Raafat Talhouk
This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under…
Homogenized description of defect modes in periodic structures with localized defects
Vincent Duchêne, Iva Vukićević, Michael I. Weinstein
A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays in amplitude as time advances. Th…
Decoupled and unidirectional asymptotic models for the propagation of internal waves
Vincent Duchene
We study the relevance of various scalar equations, such as inviscid Burgers', Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptot…
Scattering and Localization Properties of Highly Oscillatory Potentials
Vincent Duchêne, Iva Vukićević, Michael I. Weinstein
We investigate scattering, localization and dispersive time-decay properties for the one-dimensional Schrödinger equation with a rapidly oscillating and spatially localized potenti…