{"title":"Dispersive decay bound of small data solutions to Kawahara equation in a finite time scale","authors":"Jongwon Lee","doi":"10.1007/s00028-024-00980-9","DOIUrl":null,"url":null,"abstract":"<p>In this article, we prove that small localized data yield solutions to Kawahara-type equations which have linear dispersive decay on a finite time scale depending on the size of the initial data. We use the similar method used by Ifrim and Tataru to derive the dispersive decay bound of the solutions to the KdV equation, with some steps being simpler. This result is expected to be the first result of the small data global bounds of the fifth-order dispersive equations with quadratic nonlinearity.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Evolution Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00028-024-00980-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we prove that small localized data yield solutions to Kawahara-type equations which have linear dispersive decay on a finite time scale depending on the size of the initial data. We use the similar method used by Ifrim and Tataru to derive the dispersive decay bound of the solutions to the KdV equation, with some steps being simpler. This result is expected to be the first result of the small data global bounds of the fifth-order dispersive equations with quadratic nonlinearity.
期刊介绍：
The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications.
Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field.
Particular topics covered by the journal are:
Linear and Nonlinear Semigroups
Parabolic and Hyperbolic Partial Differential Equations
Reaction Diffusion Equations
Deterministic and Stochastic Control Systems
Transport and Population Equations
Volterra Equations
Delay Equations
Stochastic Processes and Dirichlet Forms
Maximal Regularity and Functional Calculi
Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations
Evolution Equations in Mathematical Physics
Elliptic Operators
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