{"title":"汉堡系统的遍历性","authors":"S. Peszat, K. Twardowska, J. Zabczyk","doi":"10.31390/josa.2.3.10","DOIUrl":null,"url":null,"abstract":"We consider a stochastic version of a system of coupled two equations formulated by Burgers with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness of the solution as well as the irreducibility property of such system were given by Twardowska and Zabczyk. In the paper the existence of a unique invariant measure is investigated. The paper generalizes the results of Da Prato, Debussche and Temam, and Da Prato and Gatarek, dealing with one equation describing the turbulent motion only.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ergodicity of Burgers' System\",\"authors\":\"S. Peszat, K. Twardowska, J. Zabczyk\",\"doi\":\"10.31390/josa.2.3.10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a stochastic version of a system of coupled two equations formulated by Burgers with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness of the solution as well as the irreducibility property of such system were given by Twardowska and Zabczyk. In the paper the existence of a unique invariant measure is investigated. The paper generalizes the results of Da Prato, Debussche and Temam, and Da Prato and Gatarek, dealing with one equation describing the turbulent motion only.\",\"PeriodicalId\":263604,\"journal\":{\"name\":\"Journal of Stochastic Analysis\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Stochastic Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31390/josa.2.3.10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Stochastic Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31390/josa.2.3.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider a stochastic version of a system of coupled two equations formulated by Burgers with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness of the solution as well as the irreducibility property of such system were given by Twardowska and Zabczyk. In the paper the existence of a unique invariant measure is investigated. The paper generalizes the results of Da Prato, Debussche and Temam, and Da Prato and Gatarek, dealing with one equation describing the turbulent motion only.
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