Unique Continuation and Observability Estimates for 2-D Stokes Equations with the Navier Slip Boundary Condition

This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an observability estimate for this equation from a subset of positive measure in time follows from the aforementioned unique continuation estimate and the new strategy developed in [16]. Several applications of the above-mentioned observability estimate to control problems of the Stokes equations are given.