The backward two-dimensional stochastic Navier-Stokes equations (BSNSEs, for short) with suitable perturbations are studied in this paper, over bounded domains for incompressible fluid flow. A priori estimates for adapted solutions of the BSNSEs are obtained which reveal a pathwise L∞ (H) bound on the solutions. The existence and uniqueness of solutions are proved by using a monotonicity argument for bounded terminal data. The continuity of the adapted solutions with respect to the terminal data is also established. © 2008 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Stochastic Processes and their Applications
Sundar, P., & Yin, H. (2009). Existence and uniqueness of solutions to the backward 2D stochastic Navier-Stokes equations. Stochastic Processes and their Applications, 119 (4), 1216-1234. https://doi.org/10.1016/j.spa.2008.06.007