Establishes global well-posedness, optimal density decay, and modified scattering for small solutions of the critical Kohn-Sham equation in d=2,3, resolving Pusateri-Sigal conjectures by extending scalar scattering theory to density matrices.
Smith,Phase mixing for the Hartree equation and Landau damping in the semi- classical limit
3 Pith papers cite this work. Polarity classification is still indexing.
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math.AP 3years
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Nonlinear Landau damping and asymptotic stability are established for translation-invariant Hartree-Fock equilibria with off-diagonal exchange in R^d for d at least 3.
Global well-posedness holds for the Alber equation in H¹𝔖¹(𝕋) for non-negative self-adjoint data, with energy conservation and polynomial growth bounds on perturbations of stable backgrounds.
citing papers explorer
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Modified Scattering for the Time-Dependent Kohn--Sham Equation
Establishes global well-posedness, optimal density decay, and modified scattering for small solutions of the critical Kohn-Sham equation in d=2,3, resolving Pusateri-Sigal conjectures by extending scalar scattering theory to density matrices.
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Asymptotic Stability of Hartree--Fock Homogenous Equilibria in $\mathbb{R}^d$
Nonlinear Landau damping and asymptotic stability are established for translation-invariant Hartree-Fock equilibria with off-diagonal exchange in R^d for d at least 3.
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Global solutions for the Alber equation in $H^1\mathfrak{S}^1(\mathbb{T})$
Global well-posedness holds for the Alber equation in H¹𝔖¹(𝕋) for non-negative self-adjoint data, with energy conservation and polynomial growth bounds on perturbations of stable backgrounds.