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.