  In this paper, a well-posed simultaneous space-time First Order System Least
Squares formulation is constructed of the instationary incompressible Stokes
equations with slip boundary conditions. As a consequence of this
well-posedness, the minimization over any conforming triple of finite element
spaces for velocities, pressure and stress tensor gives a quasi-best
approximation from that triple. The formulation is practical in the sense that
all norms in the least squares functional can be efficiently evaluated. Being
of least squares type, the formulation comes with an efficient and reliable a
posteriori error estimator. In addition, a priori error estimates are derived,
and numerical results are presented.
