{"title":"随机三维全局修正Navier-Stokes方程解的渐近行为","authors":"C. T. Anh, N. Thanh, Phan Thi Hong Tuyet","doi":"10.1080/17442508.2022.2147005","DOIUrl":null,"url":null,"abstract":"We consider 3D stochastic globally modified Navier–Stokes equations in bounded domains with homogeneous Dirichlet boundary conditions and infinite dimensional Wiener process. We study stability properties of stationary solutions. We also show that one can stabilize an unstable stationary solution by using a multiplicative Itô noise of sufficient intensity or a linear internal feedback controller with support large enough.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"90 7 1","pages":"997 - 1021"},"PeriodicalIF":1.1000,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Asymptotic behaviour of solutions to stochastic three-dimensional globally modified Navier–Stokes equations\",\"authors\":\"C. T. Anh, N. Thanh, Phan Thi Hong Tuyet\",\"doi\":\"10.1080/17442508.2022.2147005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider 3D stochastic globally modified Navier–Stokes equations in bounded domains with homogeneous Dirichlet boundary conditions and infinite dimensional Wiener process. We study stability properties of stationary solutions. We also show that one can stabilize an unstable stationary solution by using a multiplicative Itô noise of sufficient intensity or a linear internal feedback controller with support large enough.\",\"PeriodicalId\":50447,\"journal\":{\"name\":\"Finance and Stochastics\",\"volume\":\"90 7 1\",\"pages\":\"997 - 1021\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-11-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finance and Stochastics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2022.2147005\",\"RegionNum\":2,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"BUSINESS, FINANCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finance and Stochastics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1080/17442508.2022.2147005","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
Asymptotic behaviour of solutions to stochastic three-dimensional globally modified Navier–Stokes equations
We consider 3D stochastic globally modified Navier–Stokes equations in bounded domains with homogeneous Dirichlet boundary conditions and infinite dimensional Wiener process. We study stability properties of stationary solutions. We also show that one can stabilize an unstable stationary solution by using a multiplicative Itô noise of sufficient intensity or a linear internal feedback controller with support large enough.
期刊介绍:
The purpose of Finance and Stochastics is to provide a high standard publication forum for research
- in all areas of finance based on stochastic methods
- on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance.
Finance and Stochastics encompasses - but is not limited to - the following fields:
- theory and analysis of financial markets
- continuous time finance
- derivatives research
- insurance in relation to finance
- portfolio selection
- credit and market risks
- term structure models
- statistical and empirical financial studies based on advanced stochastic methods
- numerical and stochastic solution techniques for problems in finance
- intertemporal economics, uncertainty and information in relation to finance.