{"title":"气压涡度方程在球面上的一类解的稳定性","authors":"Yuri N. Skiba","doi":"10.4310/dpde.2024.v21.n3.a1","DOIUrl":null,"url":null,"abstract":"The linear and nonlinear stability of modons and Wu-Verkley waves, which are weak solutions of the barotropic vorticity equation on a rotating sphere, are analyzed. Necessary conditions for normal mode instability are obtained, the growth rate of unstable modes is estimated, and the orthogonality of unstable modes to the basic flow is shown. The Liapunov instability of dipole modons in the norm associated with enstrophy is proven.","PeriodicalId":50562,"journal":{"name":"Dynamics of Partial Differential Equations","volume":"2014 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability of a class of solutions of the barotropic vorticity equation on a sphereequation on a sphere\",\"authors\":\"Yuri N. Skiba\",\"doi\":\"10.4310/dpde.2024.v21.n3.a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The linear and nonlinear stability of modons and Wu-Verkley waves, which are weak solutions of the barotropic vorticity equation on a rotating sphere, are analyzed. Necessary conditions for normal mode instability are obtained, the growth rate of unstable modes is estimated, and the orthogonality of unstable modes to the basic flow is shown. The Liapunov instability of dipole modons in the norm associated with enstrophy is proven.\",\"PeriodicalId\":50562,\"journal\":{\"name\":\"Dynamics of Partial Differential Equations\",\"volume\":\"2014 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dynamics of Partial Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/dpde.2024.v21.n3.a1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamics of Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/dpde.2024.v21.n3.a1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Stability of a class of solutions of the barotropic vorticity equation on a sphereequation on a sphere
The linear and nonlinear stability of modons and Wu-Verkley waves, which are weak solutions of the barotropic vorticity equation on a rotating sphere, are analyzed. Necessary conditions for normal mode instability are obtained, the growth rate of unstable modes is estimated, and the orthogonality of unstable modes to the basic flow is shown. The Liapunov instability of dipole modons in the norm associated with enstrophy is proven.
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