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Chemetov, Nikolai, and Fernanda Cipriano. "Well-posedness of stochastic second grade fluids." JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 454 (2017): 585-616. Abstract

{The theory of turbulent Newtonian fluids shows that the choice of the boundary condition is a relevant issue because it can modify the behavior of a fluid by creating or avoiding a strong boundary layer. In this study, we consider stochastic second grade fluids filling a two-dimensional bounded domain with the Navier-slip boundary condition (with friction). We prove the well-posedness of this problem and establish a stability result. Our stochastic model involves a multiplicative white noise and a convective term with third order derivatives, which significantly complicate the analysis. (C) 2017 Elsevier Inc. All rights reserved.}