{"title":"广义表面准地心吸力方程的慢行波解","authors":"","doi":"10.1016/j.jfa.2024.110570","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation. Firstly we obtain the existence of a new family of global solutions via the variational method. Secondly we show the uniqueness of maximizers under our variational setting. Thirdly by using the variational framework, the uniqueness of maximizers and a concentration-compactness principle we establish some stability theorems. Moreover, after a suitable transformation, these solutions constitute the desingularization of traveling point vortex pairs.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation\",\"authors\":\"\",\"doi\":\"10.1016/j.jfa.2024.110570\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation. Firstly we obtain the existence of a new family of global solutions via the variational method. Secondly we show the uniqueness of maximizers under our variational setting. Thirdly by using the variational framework, the uniqueness of maximizers and a concentration-compactness principle we establish some stability theorems. Moreover, after a suitable transformation, these solutions constitute the desingularization of traveling point vortex pairs.</p></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123624002581\",\"RegionNum\":2,\"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":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123624002581","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation
In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation. Firstly we obtain the existence of a new family of global solutions via the variational method. Secondly we show the uniqueness of maximizers under our variational setting. Thirdly by using the variational framework, the uniqueness of maximizers and a concentration-compactness principle we establish some stability theorems. Moreover, after a suitable transformation, these solutions constitute the desingularization of traveling point vortex pairs.
期刊介绍:
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis