Null controllablity of a stochastic Stokes system with control on the drift

Abstract:

In this paper,we consider a controlled forward stochastic Stokes system with a diagonal matrix as the coefficient of diffusion term,and the diagonal matrix elements are the same bounded stochastic process.For the situation that only one control applied to the drift term,we use the Lebeau-Robbiano type spectral inequality to establish a “partial” observability estimate result,by which we get the the corresponding finite dimensional null controllability and establish the required decay estimate.Finally we derive the null controllability of the forward stochastic Stokes system.