{"title":"Perturbation at Blow-Up Time of Self-Similar Solutions for the Modified Korteweg–de Vries Equation","authors":"Simão Correia, Raphaël Côte","doi":"10.1007/s00205-024-01969-x","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a first stability result of self-similar blow-up for the modified Korteweg–de Vries equation on the line. More precisely, given a self-similar solution and a sufficiently small regular profile, there is a unique global solution which behaves at <span>\\(t=0\\)</span> as the sum of the self-similar solution and the smooth perturbation.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"248 2","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Rational Mechanics and Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-024-01969-x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a first stability result of self-similar blow-up for the modified Korteweg–de Vries equation on the line. More precisely, given a self-similar solution and a sufficiently small regular profile, there is a unique global solution which behaves at \(t=0\) as the sum of the self-similar solution and the smooth perturbation.
期刊介绍：
The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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