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This is a Quantitative Study study.

October 19, 2025Open Access

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

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This research demonstrates optimal decay rates in the density function of Hartree equation solutions, suggesting improved scattering outcomes.

The density function of small-data solutions decays at the optimal rate for the hartree equation.
Estimates for the solution remain independent of the semi-classical parameter, enhancing applicability.
Key methodologies include the boundedness of wave operators and $L^1$--$L^$ dispersive estimates.
The outcomes highlight the significance of bootstrap arguments to achieve improved dispersive estimates.

Sonae Hadama (2025) studied this question.

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This research demonstrates optimal decay rates in the density function of Hartree equation solutions, suggesting improved scattering outcomes.