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Article: Uniform estimates for 2D quasilinear wave

TitleUniform estimates for 2D quasilinear wave
Authors
KeywordsAlinhac
Ghost weight
Quasilinear wave
Uniform boundedness
Issue Date7-Jun-2023
PublisherElsevier
Citation
Advances in Mathematics, 2023, v. 428 How to Cite?
Abstract

We consider two-dimensional quasilinear wave equations with standard null-type quadratic nonlinearities. In 2001 Alinhac proved that such systems possess global in time solutions for compactly supported initial data with sufficiently small Sobolev norm. The highest norm of the constructed solution grows polynomially in time. In this work we develop a new strategy and prove uniform boundedness of the highest order norm of the solution for all time.


Persistent Identifierhttp://hdl.handle.net/10722/337346
ISSN
2023 Impact Factor: 1.5
2023 SCImago Journal Rankings: 2.022
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLi, Dong-
dc.date.accessioned2024-03-11T10:20:11Z-
dc.date.available2024-03-11T10:20:11Z-
dc.date.issued2023-06-07-
dc.identifier.citationAdvances in Mathematics, 2023, v. 428-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/10722/337346-
dc.description.abstract<p>We consider two-dimensional quasilinear wave equations with standard null-type quadratic nonlinearities. In 2001 Alinhac proved that such systems possess global in time solutions for compactly supported <a href="https://www.sciencedirect.com/topics/mathematics/initial-datum" title="Learn more about initial data from ScienceDirect's AI-generated Topic Pages">initial data</a> with sufficiently small Sobolev norm. The highest norm of the constructed solution grows polynomially in time. In this work we develop a new strategy and prove uniform <a href="https://www.sciencedirect.com/topics/mathematics/boundedness" title="Learn more about boundedness from ScienceDirect's AI-generated Topic Pages">boundedness</a> of the highest order norm of the solution for all time.<br></p>-
dc.languageeng-
dc.publisherElsevier-
dc.relation.ispartofAdvances in Mathematics-
dc.subjectAlinhac-
dc.subjectGhost weight-
dc.subjectQuasilinear wave-
dc.subjectUniform boundedness-
dc.titleUniform estimates for 2D quasilinear wave-
dc.typeArticle-
dc.identifier.doi10.1016/j.aim.2023.109157-
dc.identifier.scopuseid_2-s2.0-85161258766-
dc.identifier.volume428-
dc.identifier.isiWOS:001018587600001-
dc.identifier.issnl0001-8708-

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