2D backward stochastic Navier-Stokes equations with nonlinear forcing

The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Brownian motion. We use the spectral approximation and the truncation and variational techniques. The methodology features an interactive analysis on the basis of the regularity of the deterministic Navier-Stokes dynamics and the stochastic properties of the Itô-type diffusion processes.