Stochastic 2-D Navier-Stokes Equation with Artificial Compressibility
  In this paper we study the stochastic Navier-Stokes equation with artificial compressibility. The main results of this work are the existence and uniqueness theorem for strong solutions and the limit to incompressible flow. These results are obtained by utilizing a local monotonicity property of the sum of the Stokes operator and the nonlinearity. 
Utpal Manna, Jose-Luis Menaldi, and Sivaguru S. Sritharan