VORTICITY-VELOCITY FORMULATION OF THE STOKES PROBLEM WITH VARIABLE-DENSITY AND VISCOSITY

We investigate the vorticity-velocity formulation of the stationary, t wo-dimensional Stokes problem, in the case of variable density and vis cosity. The analysis is presented in the low Mach number regime, where the density is independent from spatial variations of the pressure. W e establish the equivalence of the vorticity-velocity and velocity-pre ssure formulations in appropriate functional spaces. When the spatial variations of the density and of the viscosity are small enough, we th en prove the existence and uniqueness of the solution to the Stokes pr oblem in both vorticity-velocity and velocity-pressure form.