  We consider the widely used continuous $\mathcal{Q}_{k}$-$\mathcal{Q}_{k-1}$
quadrilateral or hexahedral Taylor-Hood elements for the finite element
discretization of the Stokes and generalized Stokes systems in two and three
spatial dimensions. For the fast solution of the corresponding symmetric, but
indefinite system of finite element equations, we propose and analyze
matrix-free monolithic geometric multigrid solvers that are based on
appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on
results by Sch\"oberl and Zulehner (2003). We present and discuss several
numerical results for typical benchmark problems.
