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Modified scattering for long-range Hartree equations of infinite rank near vacuum

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arxiv 2408.15860 v1 pith:WW447OA4 submitted 2024-08-28 math.AP math-phmath.MP

classification math.APmath-phmath.MP
keywords decaydensityfunctionhartreenearphasevacuumapproach
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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, which consists of independently deriving the sharp dispersive decay estimates for the density function and establishing the boundedness of energy norms. The global in time well-posedness is done without introducing the phase correction, while the phase modification is explicit in terms of the density function.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Semi-classical limit of quantum scattering states for the nonlinear Hartree equation

    math.AP 2025-07 conditional novelty 8.0 of 10

    Quantum scattering states for the nonlinear Hartree equation converge, via Wigner transforms, to classical Vlasov scattering states in the semiclassical limit, with new uniform-in-Planck-constant dispersion estimates ...

  2. Uniform dispersive estimates for the semi-classical Hartree equation with long-range interaction

    math.AP 2025-07 reject novelty 7.0 of 10

    Small-data solutions of the semiclassical Hartree equation with long-range interaction satisfy the uniform-in-hbar optimal density decay ||rho(t)||_{L∞} ≲ <t>^{-3}.

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