4 papers
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…