107 citations · 133 across the 10 of their papers we have counts for
12 papers
On weakly turbulent solutions to the perturbed linear Harmonic oscillator
Erwan Faou, Pierre Raphael
We introduce specific solutions to the linear harmonic oscillator, named bubbles. They form resonant families of invariant tori of the linear dynamics, with arbitrarily large Sobol…
On blow up for the energy super critical defocusing non linear Schrödinger equations
Frank Merle, Pierre Raphael, Igor Rodnianski +1
We consider the energy supercritical defocusing nonlinear Schrödinger equation in dimension . In a suitable range of energy supercritical par…
Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations
Yakine Bahri, Yvan Martel, Pierre Raphaël
We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schrödinger equation on , close…
On travelling waves of the non linear Schrödinger equation escaping a potential well
Ivan Naumkin, Pierre Raphäel
In this paper we consider the NLS equation with focusing nonlinearities in the presence of a potential. We investigate the compact soliton motions that correspond to a free soliton…
On small travelling waves to the mass critical fractional NLS
Ivan Naumkin, Pierre Raphaël
We consider the mass critical fractional (NLS). We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associate…
On the stability of critical chemotactic aggregation
Pierre Raphael, Remi Schweyer
We consider the two dimensional parabolic-elliptic Patlak-Keller-Segel model of chemotactic aggregation for radially symmetric initial data. We show the existence of a stable mecha…