REVIEW 2 cited by
Modified scattering for long-range Hartree equations of infinite rank near vacuum
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
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.
Forward citations
Cited by 2 Pith papers
-
Semi-classical limit of quantum scattering states for the nonlinear Hartree equation
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 ...
-
Uniform dispersive estimates for the semi-classical Hartree equation with long-range interaction
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}.
Discussion (0). Continue with ORCID to comment.