  In this work we treat the space-time discretization of the generalized Stokes
equations in the case of Dirichlet boundary conditions. We prove error
estimates in the case $p\in[\frac{2d}{d+2},\infty)$ that are independent of the
degeneracy parameter $\delta\in[0,\delta_0]$. For $p\leq 2$, our convergence
rate is optimal.
