10 citations · 16 across the 10 of their papers we have counts for
12 papers · 1 filter
Absence of embedded spectrum for nonlinear Schrödinger equations linearized around one dimensional ground states
Charles Collot, Pierre Germain, Eliot Pacherie
We consider the nonlinear Schrödinger equation in dimension one for a generic nonlinearity. We show that ground states do not have embedded eigenvalues in the essential spectrum of…
Estimates for the Gross-Pitaevskii equation linearized around a vortex
Charles Collot, Pierre Germain, Eliot Pacherie
We consider the linearized two-dimensional Gross-Pitaevskii equation around a vortex of degree one, with data in the same equivariance class. Various estimates are proved for the s…
Nested discontinuous asymptotic profiles for the viscous Burgers equation with infinite mass
Nicola de Nitti, Eliot Pacherie
We study the viscous Burgers equation with a family of initial data having infinite mass. After rescaling, the solution converges toward a bounded discontinuous profile in the long…
Stability Analysis of a Non-Separable Mean-Field Games for Pedestrian Flow in Large Corridors
Mohamed Ghattassi, Nader Masmoudi, Eliot Pacherie
We investigate the existence and stability of small perturbations of constant states of the generalized Hughes model for pedestrian flow in an infinitely large corridor. We show th…
On the Number of Normalized Ground State Solutions for a class of Elliptic Equations with general nonlinearities and potentials
Hichem Hajaiej, Eliot Pacherie, Linjie Song
We provide a precise description of the set of normalized ground state solutions (NGSS) for the class of elliptic equations: $$ -Δu - λu + V (| x |) u - f (| x |, u) = 0,\quad\text…
Nonlinear enhanced dissipation in viscous Burgers type equations II
Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie
In this follow up paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of inf…
Nonlinear enhanced dissipation in viscous Burgers type equations
Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in th…
Localisation of perturbations of a constant state in a traffic flow model
Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larg…
A uniqueness result for the two vortex travelling wave in the Nonlinear Schrodinger equation
David Chiron, Eliot Pacherie
For the Nonlinear Schrodinger equation in dimension 2, the existence of a global minimizer of the energy at fixed momentum has been established by Bethuel-Gravejat-Saut. This minim…
On the stability of the Ginzburg-Landau vortex
Philippe Gravejat, Eliot Pacherie, Didier Smets
We introduce a functional framework taylored to investigate the minimality and stability properties of the Ginzburg-Landau vortex of degree one on the whole plane. We prove that a…
Coercivity for travelling waves in the Gross-Pitaevskii equation in for small speed
David Chiron, Eliot Pacherie
In the previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some…
Smooth branch of travelling waves for the Gross-Pitaevskii equation in for small speed
David Chiron, Eliot Pacherie
We construct a smooth branch of travelling wave solutions for the 2 dimensional Gross-Pitaevskii equations for small speed. These travelling waves exhibit two vortices far away fro…