Vorticity-velocity formulations of the Stokes problem in 3D

This work studies the three-dimensional Stokes problem expressed in terms o f vorticity and velocity variables. We make general assumptions on the regu larity and the topological structure of the flow domain: the boundary is Li pschitz and possibly non-connected and the flow domain may be multiply conn ected. Upon introducing a new variational space for the vorticity, five wea k formulations of the Stokes problem are obtained. All the formulations are shown to lead to well-posed problems and to be equivalent to the primitive variable formulation. The various formulations are discussed by interpreti ng the rest functions for the vorticity (resp. velocity) equation as vector potentials for the velocity (resp, vorticity). Of the five sets of boundar y conditions derived in the paper, three are already known, but only for do mains with a trivial topological structure, while the remaining two are new . Copyright (C) 1999 John Wiley & Sons.