In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated with the impulse control problem are resolved in a weak sense, using semigroup approach with a convergence uniform over path.
Numerical Analysis and Computation | Probability
J.-L. Menaldi and S. S. Sritharan, Impulse control of stochastic Navier-Stokes equations, Nonlinear Analysis, 52 (2003), 357-381. doi: 10.1016/S0362-546X(01)00722-2