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math.AP2025
Uniform dispersive estimates for the semi-classical Hartree equation with long-range interaction
Sonae Hadama
In this paper, we consider the Hartree equation with smooth but long-range interaction in the semi-classical regime, in three-dimensional space. We show that the density function o…
math.AP2025
Semi-classical limit of quantum scattering states for the nonlinear Hartree equation
Sonae Hadama, Younghun Hong
This article concerns the long-time dynamics of quantum particles in the semi-classical regime. First, we show that for the nonlinear Hartree equation with short-range interaction…
math.AP2025
Scattering for the positive density Hartree equation
Antoine Borie, Sonae Hadama, Julien Sabin
We study the asymptotic stability for large times of homogeneous stationary states for the nonlinear Hartree equation for density matrices in Rd for d\geq3. We can reach both the o…