SCATTERING AND NONSCATTERING OF THE HARTREE-TYPE NONLINEAR DIRAC SYSTEM AT CRITICAL REGULARITY

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dc.contributor.authorCho, Yonggeunko
dc.contributor.authorHong, Seokchangko
dc.contributor.authorLee, Kiyeonko
dc.date.accessioned2023-12-10T05:04:10Z-
dc.date.available2023-12-10T05:04:10Z-
dc.date.created2023-12-08-
dc.date.created2023-12-08-
dc.date.created2023-12-08-
dc.date.issued2023-
dc.identifier.citationSIAM JOURNAL ON MATHEMATICAL ANALYSIS, v.55, no.4, pp.3395 - 3419-
dc.identifier.issn0036-1410-
dc.identifier.urihttp://hdl.handle.net/10203/316192-
dc.description.abstractWe consider Cauchy problem of Hartree-type nonlinear Dirac equation with potentials given by Vb(x) = 1 e-b|x|/4π |x| (b≥0). In previous works regarding a global well-posedness of Dirac equation with these potentials, a standard argument is to utilize null form estimates in order to prove global well-posedness for Hs-data, s > 0. However, the null structure inside the equations is not enough to attain critical regularity. We impose an extra regularity assumption with respect to the angular variable. First, we prove the global well-posedness and scattering of Dirac equations with Hartree-type nonlinearity for b > 0 for small L2x-data with additional angular regularity. We also show that only a small amount of angular regularity is required to obtain the global existence of solutions. Second, we obtain nonscattering result for a certain class of solutions with the Coulomb potential V0(x). 4π | x| (b≥0). In previous works regarding a global well-posedness of Dirac equation with these potentials, a standard argument is to utilize null form estimates in order to prove global well-posedness for Hs-data, s > 0. However, the null structure inside the equations is not enough to attain critical regularity. We impose an extra regularity assumption with respect to the angular variable. First, we prove the global well-posedness and scattering of Dirac equations with Hartree-type nonlinearity for b > 0 for small L2x-data with additional angular regularity. We also show that only a small amount of angular regularity is required to obtain the global existence of solutions. Second, we obtain nonscattering result for a certain class of solutions with the Coulomb potential V0(x). © 2023 Society for Industrial and Applied Mathematics.-
dc.languageEnglish-
dc.publisherSIAM PUBLICATIONS-
dc.titleSCATTERING AND NONSCATTERING OF THE HARTREE-TYPE NONLINEAR DIRAC SYSTEM AT CRITICAL REGULARITY-
dc.typeArticle-
dc.identifier.wosid001114782600022-
dc.identifier.scopusid2-s2.0-85169884660-
dc.type.rimsART-
dc.citation.volume55-
dc.citation.issue4-
dc.citation.beginningpage3395-
dc.citation.endingpage3419-
dc.citation.publicationnameSIAM JOURNAL ON MATHEMATICAL ANALYSIS-
dc.identifier.doi10.1137/21M1437135-
dc.contributor.localauthorLee, Kiyeon-
dc.contributor.nonIdAuthorCho, Yonggeun-
dc.contributor.nonIdAuthorHong, Seokchang-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorAngular regularity-
dc.subject.keywordAuthorCoulomb potential-
dc.subject.keywordAuthorDirac equation-
dc.subject.keywordAuthorGlobal well-posedness-
dc.subject.keywordAuthorNull structure-
dc.subject.keywordAuthorScattering-
dc.subject.keywordAuthorU&lt-
dc.subject.keywordAuthorsup&gt-
dc.subject.keywordAuthorp&lt-
dc.subject.keywordAuthor/sup&gt-
dc.subject.keywordAuthor- V&lt-
dc.subject.keywordAuthorsup&gt-
dc.subject.keywordAuthorp&lt-
dc.subject.keywordAuthor/sup&gt-
dc.subject.keywordAuthorspace-
dc.subject.keywordAuthorYukawa potential-
dc.subject.keywordPlusWELL-POSEDNESS-
dc.subject.keywordPlusNULL STRUCTURE-
dc.subject.keywordPlusEQUATIONS-
dc.subject.keywordPlusEXISTENCE-
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