Variational approaches to the two-dimensional Stokes system in terms of the vorticity (Q1184427)

The aim of this work is to present a rigorous variational framework for the two-dimensional Stokes problem in terms of the vorticity, together with the stream function or the velocity. Such a study serves as a basis for the more important case of three-dimensional problems, to be treated in a forthcoming paper. On the other hand it gives relevant indications on what should be done, to solve numerically the incompressible Navier- Stokes equations in the velocity-vorticity formulation. As it should be noted, though attractive, the use of this approach requires much care, especially as far as the mass conservation law is concerned.