{"title":"三维及更高维Zakharov-Kuznetsov方程的次临界适定性结果","authors":"S. Herr, S. Kinoshita","doi":"10.5802/aif.3547","DOIUrl":null,"url":null,"abstract":"The Zakharov-Kuznetsov equation in space dimension $d\\geq 3$ is considered. It is proved that the Cauchy problem is locally well-posed in $H^s(\\mathbb{R}^d)$ in the full subcritical range $s>(d-4)/2$, which is optimal up to the endpoint. As a corollary, global well-posedness in $L^2(\\mathbb{R}^3)$ and, under a smallness condition, in $H^1(\\mathbb{R}^4)$, follow.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Subcritical well-posedness results for the Zakharov–Kuznetsov equation in dimension three and higher\",\"authors\":\"S. Herr, S. Kinoshita\",\"doi\":\"10.5802/aif.3547\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Zakharov-Kuznetsov equation in space dimension $d\\\\geq 3$ is considered. It is proved that the Cauchy problem is locally well-posed in $H^s(\\\\mathbb{R}^d)$ in the full subcritical range $s>(d-4)/2$, which is optimal up to the endpoint. As a corollary, global well-posedness in $L^2(\\\\mathbb{R}^3)$ and, under a smallness condition, in $H^1(\\\\mathbb{R}^4)$, follow.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/aif.3547\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/aif.3547","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Subcritical well-posedness results for the Zakharov–Kuznetsov equation in dimension three and higher
The Zakharov-Kuznetsov equation in space dimension $d\geq 3$ is considered. It is proved that the Cauchy problem is locally well-posed in $H^s(\mathbb{R}^d)$ in the full subcritical range $s>(d-4)/2$, which is optimal up to the endpoint. As a corollary, global well-posedness in $L^2(\mathbb{R}^3)$ and, under a smallness condition, in $H^1(\mathbb{R}^4)$, follow.
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