International Journal of Stochastic Analysis
Volume 2010 (2010), Article ID 730492, 24 pages
Research Article

Stochastic Navier-Stokes Equations with Artificial Compressibility in Random Durations

Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA

Received 1 December 2009; Accepted 11 May 2010

Academic Editor: Jiongmin M. Yong

Copyright © 2010 Hong Yin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.