5 papers · 1 filter
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…
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…
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 semil…
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,…