{"title":"Wave-breaking and persistence properties in weighted $$L^p$$ spaces for a Camassa–Holm type equation with quadratic and cubic nonlinearities","authors":"Wenguang Cheng, Ji Lin","doi":"10.1007/s00605-023-01938-8","DOIUrl":null,"url":null,"abstract":"<p>We consider the Cauchy problem of a Camassa–Holm type equation with quadratic and cubic nonlinearities. We establish a new sufficient condition on the initial data that leads to the wave-breaking for this equation. Moreover, we obtain the persistence results of solutions for the equation in weighted <span>\\(L^p\\)</span> spaces.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"215 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-023-01938-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We consider the Cauchy problem of a Camassa–Holm type equation with quadratic and cubic nonlinearities. We establish a new sufficient condition on the initial data that leads to the wave-breaking for this equation. Moreover, we obtain the persistence results of solutions for the equation in weighted \(L^p\) spaces.
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