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Multilinear oscillatory integrals and estimates for coupled systems of dispersive partial differential equations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Partial Differential Equations.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Partial Differential Equations.ORCID iD: 0000-0001-8332-6302
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We establish sharp global regularity of a class of multilinear oscillatory integral operators that are associated to nonlinear dispersive equations with both Banach and quasi-Banach target spaces. As a consequence we also prove the (local in time) continuous dependence on the initial data for solutions of a large class of coupled systems of dispersive partial differential equations.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-498298OAI: oai:DiVA.org:uu-498298DiVA, id: diva2:1743070
Available from: 2023-03-13 Created: 2023-03-13 Last updated: 2023-04-21Bibliographically approved
In thesis
1. Regularity of multilinear oscillatory integral operators and nonlinear dispersive partial differential equations
Open this publication in new window or tab >>Regularity of multilinear oscillatory integral operators and nonlinear dispersive partial differential equations
2023 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We show regularity of multilinear Schrödinger integral operators as well as multilinear oscillatory integrals with connection to dispersive partial differential equations. These results are used to show regularity of a system of nonlinear dispersive partial differential equations.
Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2023. p. 61
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 130
Keywords
oscillatory integral operators, partial differential equations
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-500277 (URN)978-91-506-3006-0 (ISBN)
Public defence
2023-06-02, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2023-05-09 Created: 2023-04-14 Last updated: 2023-05-09

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Bergfeldt, AkselStaubach, Wolfgang

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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Language
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  • en-US
  • fi-FI
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  • nn-NB
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Output format
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  • rtf
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