{"title":"Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case","authors":"Jacek Jendrej, Andrew Lawrie","doi":"10.1007/s40818-023-00159-4","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions <span>\\(D \\ge 4\\)</span>. This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution <i>W</i>, called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"9 2","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-023-00159-4.pdf","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-023-00159-4","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions \(D \ge 4\). This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution W, called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.
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