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L<sup>p</sup> BOUNDEDNESS OF THE SCATTERING WAVE OPERATORS OF SCHRÖDINGER DYNAMICS WITH TIME-DEPENDENT POTENTIALS AND APPLICATIONS–PART I

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dc.contributor.authorSoffer, Avyen
dc.contributor.authorWu, Xiaoxuen
dc.date.accessioned2026-07-03T22:43:09Z
dc.date.available2026-07-03T22:43:09Z
dc.date.issued2025en
dc.description.abstractThis paper establishes the Lp boundedness of wave operators localized at high-frequency for linear Schrödinger equations in R3 with time-dependent potentials. The approach to the proof is based on new cancellation lemmas. As a typical application based on this method, combined with Strichartz estimates is the existence and scattering for nonlinear dispersive equations. For example, we prove global existence and uniform boundedness in L∞, for a class of Hartree nonlinear Schrödinger equations in L2(R3), allowing the presence of solitons. We also prove the existence of free channel wave operators in Lp(R3) for p > 6.en
dc.description.sponsorshipReceived by the editors March 4, 2022, and, in revised form, January 20, 2023, and December 16, 2024. 2020 Mathematics Subject Classification. Primary 35P25, 35Q55, 47A40. The first author was supported in part by NSF grant DMS-1600749 and by NSFC11671163. The second author is supported by ARC-FL220100072.en
dc.description.statusPeer-revieweden
dc.format.extent71en
dc.identifier.issn0002-9947en
dc.identifier.otherORCID:/0000-0003-2972-8153/work/219173146en
dc.identifier.scopus105005746723en
dc.identifier.urihttps://hdl.handle.net/1885/733812758
dc.language.isoenen
dc.rightsPublisher Copyright: © 2025 American Mathematical Society.en
dc.sourceTransactions of the American Mathematical Societyen
dc.titleL<sup>p</sup> BOUNDEDNESS OF THE SCATTERING WAVE OPERATORS OF SCHRÖDINGER DYNAMICS WITH TIME-DEPENDENT POTENTIALS AND APPLICATIONS–PART Ien
dc.typeJournal articleen
dspace.entity.typePublicationen
local.bibliographicCitation.lastpage4507en
local.bibliographicCitation.startpage4437en
local.contributor.affiliationSoffer, Avy; Rutgers - The State University of New Jersey, New Brunswicken
local.contributor.affiliationWu, Xiaoxu; Mathematical Sciences Institute Research, Mathematical Sciences Institute, ANU College of Systems and Society, The Australian National Universityen
local.identifier.citationvolume378en
local.identifier.doi10.1090/tran/9414en
local.identifier.pure7f5b004a-0e00-4f13-8cdf-9a926dfbf5e7en
local.identifier.urlhttps://www.scopus.com/pages/publications/105005746723en
local.type.statusPublisheden

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