Stochastic Navier-Stokes Equations with Artificial Compressibility in Random Durations

Abstract EN

The existence and uniqueness of adapted solutions to the backward stochastic Navier-Stokes equation with artificial compressibility in two-dimensional bounded domains are shown by Minty-Browder monotonicity argument, finite-dimensional projections, and truncations.

Continuity of the solutions with respect to terminal conditions is given, and the convergence of the system to an incompressible flow is also established.