{"title":"Mean Field Equation for Vortex Filament Systems","authors":"Ken Sawada, Takashi Suzuki","doi":"10.11345/NCTAM.61.201","DOIUrl":null,"url":null,"abstract":"We consider vortex filament systems which is regarded as a three dimensional extension of the point vortex system introduced by Onsager to investigate the 2D turbulence. We show that this system is equipped with a dual variational structure as in the case of the point vortex system, and that the mean field equations for the system in terms of the stream function and the vorticity are derived from a Lagrangian. In addition, we discuss the existence of solutions to the mean field equations.","PeriodicalId":330369,"journal":{"name":"Theoretical and applied mechanics Japan","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and applied mechanics Japan","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11345/NCTAM.61.201","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider vortex filament systems which is regarded as a three dimensional extension of the point vortex system introduced by Onsager to investigate the 2D turbulence. We show that this system is equipped with a dual variational structure as in the case of the point vortex system, and that the mean field equations for the system in terms of the stream function and the vorticity are derived from a Lagrangian. In addition, we discuss the existence of solutions to the mean field equations.
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