18 citations · 23 across the 6 of their papers we have counts for
9 papers · 1 filter
Derivation of the homogeneous kinetic wave equation: longer time scales
Charles Collot, Pierre Germain
We consider the nonlinear Schrödinger equation set on a flat torus, in the regime which is conjectured to lead to the kinetic wave equation; in particular, the data are random, and…
Stability of Steady States for Hartree and Schrodinger Equations for Infinitely Many Particles
Charles Collot, Anne-Sophie de Suzzoni
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. I…
On the derivation of the homogeneous kinetic wave equation
Charles Collot, Pierre Germain
The nonlinear Schrödinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greate…
Refined description and stability for singular solutions of the 2D Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We construct solutions to the two dimensional parabolic-elliptic Keller-Segel model for chemotaxis that blow up in finite time . The solution is decomposed as the sum of a stati…
Spectral analysis for singularity formation of the two dimensional Keller-Segel system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi +1
We analyse an operator arising in the description of singular solutions to the two-dimensional Keller-Segel problem. It corresponds to the linearised operator in parabolic self-sim…
Singularities and unsteady separation for the inviscid two-dimensional Prandtl's system
Charles Collot, Tej-Eddine Ghoul, Nader Masmoudi
We consider the inviscid unsteady Prandtl system in two dimensions, motivated by the fact that it should model to leading order separation and singularity formation for the origina…