Pub Date : 2021-12-31DOI: 10.15377/2409-5761.2021.08.10
Shilun Li, H. Yin
In this paper, the authors presented a novel fluid dynamics system, the forward-backward stochastic Navier-Stokes equations in two dimensions for incompressible fluid flows. The well-posedness of the system is obtained through a two-step process. First, certain projections of the system to the finite dimensions are employed, and the existence and uniqueness of solutions in finite dimensions are proved via the four step scheme. Then the Galerkin approximation is used to show the existence and uniqueness of a solution to the system in an infinite dimensional functional setup.
{"title":"A Four Step Scheme Approach to the Forward-Backward Stochastic Navier-Stokes Equations","authors":"Shilun Li, H. Yin","doi":"10.15377/2409-5761.2021.08.10","DOIUrl":"https://doi.org/10.15377/2409-5761.2021.08.10","url":null,"abstract":"In this paper, the authors presented a novel fluid dynamics system, the forward-backward stochastic Navier-Stokes equations in two dimensions for incompressible fluid flows. The well-posedness of the system is obtained through a two-step process. First, certain projections of the system to the finite dimensions are employed, and the existence and uniqueness of solutions in finite dimensions are proved via the four step scheme. Then the Galerkin approximation is used to show the existence and uniqueness of a solution to the system in an infinite dimensional functional setup.","PeriodicalId":335387,"journal":{"name":"Journal of Advances in Applied & Computational Mathematics","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133377215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：