42 citations · 54 across the 8 of their papers we have counts for
9 papers
On the zero capillarity limit for the Euler-Korteweg system
Corentin Audiard, Marc-Antoine Vassenet
We study the Euler-Korteweg equations with a weak capillarity tensor. It formally converges to the Euler equations in the zero capillarity limit. Our aim is two-fold : first we pro…
Linear asymptotic stability of small-amplitude periodic waves of the generalized Korteweg--de Vries equations
Corentin Audiard, L. Miguel Rodrigues, Changzhen Sun
In this note, we extend the detailed study of the linearized dynamics obtained for cnoidal waves of the Korteweg--de Vries equation in \cite{JFA-R} to small-amplitude periodic trav…
On the sharp regularity of solutions to hyperbolic boundary value problems
Corentin Audiard
We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are…
About plane periodic waves of the nonlinear Schrödinger equations
Corentin Audiard, L Rodrigues
The present contribution contains a quite extensive theory for the stability analysis of plane periodic waves of general Schr{ö}dinger equations. On one hand, we put the one-dimens…
On the time of existence of solutions of the Euler-Korteweg system
Corentin Audiard
Under a natural stability condition on the pressure, it is known that for small irrotational initial data, the solutions of the Euler-Korteweg system are global in time. When the i…
Existence of multi-traveling waves in capillary fluids
Corentin Audiard
We prove the existence of multi-soliton and kink-multi-soliton solutions of the Euler-Korteweg system in dimension one. Such solutions behaves asymptotically in time like several t…
Global Strichartz estimates for the Schrödinger equation with non zero boundary conditions and applications
Corentin Audiard
We consider the Schrödinger equation on a half space in any dimension with a class of nonhomogeneous boundary conditions including Dirichlet, Neuman and the so-called transparent b…
Small energy traveling waves for the Euler-Korteweg system
Corentin Audiard
We investigate the existence and properties of traveling waves for the Euler-Korteweg system with general capillarity and pressure. Our main result is the existence in dimension tw…
Global well-posedness of the Euler-Korteweg system for small irrotational data
Corentin Audiard, Boris Haspot
The Euler-Korteweg equations are a modification of the Euler equations that takes into account capillary effects. In the general case they form a quasi-linear system that can be re…