  The purpose of this article is to introduce radial basis function, (RBFs),
methods for solving null control problems for the Stokes system with few
internal scalar controls and Dirichlet or Navier slip boundary conditions. To
the best of our knowledge, it has not been reported in the literature any
numerical approximation through RBFs to solve the direct Stokes problem with
Navier slip boundary conditions. In this paper we fill this gap to show its
application for solving the null control problem for the Stokes system. To
achieve this goal, we introduce two radial basis function solvers, one global
and the other local, to discretized the primal and adjoint systems related to
the control problem. Both techniques are based on divergence free global RBFs.
Stability analysis for these methods is performed in terms of the spectral
radius of the corresponding Gram matrices. By using a conjugate gradient
algorithm, adapted to the radial basis function setting, the control problem is
solved. Several test problems in two dimensions are numerically solved by these
RBFs methods to test their feasibility. The solutions to these problems are
also obtained by finite elements techniques, (FE), to compare their relative
performance.
