Cipriano, FernandaPereira, Diogo2019-07-242019-07-242019-07-150022-247XPURE: 12727114PURE UUID: 460c6b50-801b-4a22-aeb6-e7636ee148e2Scopus: 85063573777WOS: 000465168900049ORCID: /0000-0001-6385-8846/work/63724200http://www.scopus.com/inward/record.url?scp=85063573777&partnerID=8YFLogxKThe authors are very grateful to the institutions Fundacao Calouste Gulbenkian, and Fundacao para a Ciencia e a Tecnologia due to the financial support. The work of D. Pereira was supported by the Fundacao Calouste Gulbenkian through the program "Estimulo a Investigacao 2016", project "Monte Carlo na equagdo Hamilton-Jacobi-Bellman". The work of F. Cipriano was supported by the Fundacao Calouste Gulbenkian through the project "Monte Carlo na equagao Hamilton-Jacobi-Bellman", and Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes).This article deals with a feedback optimal control problem for the stochastic second grade fluids. More precisely, we establish the existence of an optimal feedback control for the two-dimensional stochastic second grade fluids, with Navier-slip boundary conditions. In addition, using the Galerkin approximations, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs, showing the existence of the so-called ϵ−optimal feedback control.22373410engFeedback optimal controlSecond grade fluidsStochastic differential equationϵ−Optimal feedback controlAnalysisApplied Mathematicsjournal article10.1016/j.jmaa.2019.03.064https://www.scopus.com/pages/publications/85063573777