{"title":"关于KP-I方程的适定性","authors":"Zihua Guo, Luc Molinet","doi":"10.1007/s40818-026-00235-5","DOIUrl":null,"url":null,"abstract":"<div><p>We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in <span>\\(H^{s,0}({\\mathbb R}^2)\\)</span> for <span>\\(s>3/4\\)</span> and unconditional global well-posedness in the energy space. We also prove the global existence of perturbations with finite energy of non decaying smooth global solutions.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Well-Posedness of the KP-I Equation\",\"authors\":\"Zihua Guo, Luc Molinet\",\"doi\":\"10.1007/s40818-026-00235-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in <span>\\\\(H^{s,0}({\\\\mathbb R}^2)\\\\)</span> for <span>\\\\(s>3/4\\\\)</span> and unconditional global well-posedness in the energy space. We also prove the global existence of perturbations with finite energy of non decaying smooth global solutions.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2026-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-026-00235-5\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-026-00235-5","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in \(H^{s,0}({\mathbb R}^2)\) for \(s>3/4\) and unconditional global well-posedness in the energy space. We also prove the global existence of perturbations with finite energy of non decaying smooth global solutions.
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