2 citations · 2 across the 5 of their papers we have counts for
7 papers
Asymptotic Behavior of One-Dimensional Hartree Equations with the Long-Range Interaction
Changhun Yang, Chanjin You
We investigate the long-time behavior of small solutions to the one-dimensional Hartree equation with the soft Coulomb interaction. The Hartree equation arises as an effective mean…
Modified Scattering for the Time-Dependent Kohn--Sham Equation
Masaki Kawamoto, Jinyeop Lee, Changhun Yang +1
We study the long-time behavior of the (critical) Kohn--Sham equation in two and three dimensions, i.e.,\[ \mathrm{i} \partial_t γ = \Big[-\frac{1}{2}Δ+ λ\, |\cdot|^{-1} \ast ρ_{γ}…
Asymptotic Stability of Hartree--Fock Homogenous Equilibria in
Toan T. Nguyen, Chanjin You
In this paper, we establish nonlinear Landau damping and asymptotic stability of a large class of translation-invariant steady solutions to the time-dependent Hartree--Fock equatio…
Large Time Behavior of the Klein-Gordon-Schrödinger system
Chanjin You
We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schrödinger system in three dimensions. The system consists of coupled semili…
Modified scattering for long-range Hartree equations of infinite rank near vacuum
Toan T. Nguyen, Chanjin You
We establish the asymptotic behavior and decay of solutions near vacuum to the Hartree equation with the Coulomb interaction potential in three dimensions. Our approach is direct,…
Phase mixing estimates for the nonlinear Hartree equation of infinite rank
Chanjin You
In this paper, we prove the phase mixing estimates for the density and its derivatives associated with the nonlinear Hartree equation around certain translation-invariant equilibri…
Plasmons for the Hartree equations with Coulomb interaction
Toan T. Nguyen, Chanjin You
In this work, we establish the existence and decay of {\em plasmons}, the quantum of Langmuir's oscillatory waves found in plasma physics, for the linearized Hartree equations desc…