- Two variational models of the primitive equations governing two-dimensional, viscous incompressible Stokes flows are studied. The first model contains the velocities and the pressure as dependent unknowns, while the second model contains only the velocities and is based on the Penalty Method. Existence and uniqueness of solutions to the associated variational problems are proved using the Generalized Lax-Milgram theorem of Babuska. Existence and uniqueness of approximate solution are also proved and error estimates are derived. 1978.