10 citations · 12 across the 10 of their papers we have counts for
13 papers
Splitting methods for Intermediate Long Wave and perturbed Benjamin--Ono models
Yvonne Alama Bronsard, Clémentine Courtès, Benjamin Melinand
Recently, novel integrability techniques, and most notably Birkhoff coordinates followed by an explicit formula, have been introduced to solve the Benjamin--Ono (BO) equation, lead…
Phase sinks and sources around two-dimensional periodic-wave solutions of reaction-diffusion-advection systems
Benjamin Melinand, L. Miguel Rodrigues
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assump…
Rigid Lid limit in shallow water over a flat bottom
Benjamin Melinand
We perform the so-called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green-Naghdi equations. To do so we consider an appropriate n…
Dispersive estimates for nonhomogeneous radial phases: an application to weakly dispersive equations and water wave models
Benjamin Melinand
We study linear dispersive equations in dimension one and two for a class of radial nonhomogeneous phases. L 1 L type estimates, Strichartz estimates, local…
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…
Existence and behavior of steady solutions on an interval for general hyperbolic-parabolic systems of conservation laws
Benjamin Melinand, Kevin Zumbrun
We study the inflow-outflow boundary value problem on an interval, the analog of the 1D shock tube problem for gas dynamics, for general systems of hyperbolic-parabolic conservatio…
Existence and stability of steady noncharacteristic solutions on a finite interval of full compressible Navier-Stokes equations
Blake Barker, Benjamin Melinand, Kevin Zumbrun
We treat the 1D shock tube problem, establishing existence of steady solutions of full (nonisentropic) polytropic gas dynamics with arbitrary noncharacteristic data. We present als…
Existence and stability of steady compressible Navier-Stokes solutions on a finite interval with noncharacteristic boundary conditions
Benjamin Melinand, Kevin Zumbrun
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for ge…
The KP approximation under a weak Coriolis forcing
Benjamin Melinand
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…
A Splitting Method for Deep Water with Bathymetry
Afaf Bouharguane, Benjamin Melinand
In this paper we derive and prove the wellposedness of a deep water model that generalizes the Saut-Xu system for nonflat bottoms. Then, we present a new numerical method based on…
Long wave approximation for water waves under a Coriolis forcing and the Ostrovsky equation
Benjamin Melinand
This paper is devoted to the study of the long wave approximation for water waves under the influence of the gravity and a Coriolis forcing. We start by deriving a generalization o…
Coriolis effect on water waves
Benjamin Melinand
This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow…
A mathematical study of meteo and landslide tsunamis : The Proudman resonance
Benjamin Melinand
In this paper, we want to understand the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the…