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Modified Scattering for the Hartree Nonlinear Schr\"odinger Equation

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arxiv 2407.18411 v1 pith:J3I44ZFY submitted 2024-07-25 math.AP

Tim Van Hoose This is my paper · ORCID
classification math.AP
keywords scatteringequationhartreemodifiednonlinearodingerschrbehavior
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abstract

We prove sharp $L^\infty$ decay and modified scattering for the Hartree nonlinear Schr\"odinger equation in dimensions $2$ and $3$ using the testing by wavepackets method of Ifrim and Tataru. We show that the scattering behavior happens at a regularity well below that of earlier results of Hayashi-Naumkin and Kato-Pusateri.

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  1. Long-Time Dynamics and Modified Scattering for the Coulomb Vlasov--Hartree System

    math.AP 2026-08 conditional novelty 7.0 of 10

    Small-data solutions of the three-dimensional Coulomb Vlasov-Hartree system scatter with logarithmic corrections determined by the opposite species, with explicit asymptotic profiles.

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