{"title":"无界平面域上二维NAVIER-STOKES系统吸引子上的函数的渐近性$ \\vert x\\vert\\to\\infty$","authors":"A. Babin","doi":"10.1070/SM1993V074N02ABEH003355","DOIUrl":null,"url":null,"abstract":"The Navier-Stokes system is considered in a plane domain that has several exits to infinity having the form of channels of bounded width. It is assumed that the external force decays sufficiently fast at infinity. Solutions are considered that are defined and bounded for all . Such solutions lie on an attractor of the system. An asymptotic expansion as is obtained for these solutions. The presence of this expansion indicates, in particular, that turbulence in this situation does not propagate to infinity.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"ASYMPTOTICS AS $ \\\\vert x\\\\vert\\\\to\\\\infty$ OF FUNCTIONS LYING ON AN ATTRACTOR OF THE TWO-DIMENSIONAL NAVIER-STOKES SYSTEM IN AN UNBOUNDED PLANE DOMAIN\",\"authors\":\"A. Babin\",\"doi\":\"10.1070/SM1993V074N02ABEH003355\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Navier-Stokes system is considered in a plane domain that has several exits to infinity having the form of channels of bounded width. It is assumed that the external force decays sufficiently fast at infinity. Solutions are considered that are defined and bounded for all . Such solutions lie on an attractor of the system. An asymptotic expansion as is obtained for these solutions. The presence of this expansion indicates, in particular, that turbulence in this situation does not propagate to infinity.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"15 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1993V074N02ABEH003355\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1993V074N02ABEH003355","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ASYMPTOTICS AS $ \vert x\vert\to\infty$ OF FUNCTIONS LYING ON AN ATTRACTOR OF THE TWO-DIMENSIONAL NAVIER-STOKES SYSTEM IN AN UNBOUNDED PLANE DOMAIN
The Navier-Stokes system is considered in a plane domain that has several exits to infinity having the form of channels of bounded width. It is assumed that the external force decays sufficiently fast at infinity. Solutions are considered that are defined and bounded for all . Such solutions lie on an attractor of the system. An asymptotic expansion as is obtained for these solutions. The presence of this expansion indicates, in particular, that turbulence in this situation does not propagate to infinity.
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