  Motivated by the study of the corner singularities in the so-called cavity
flow, we establish in this article, the existence and uniqueness of solutions
in $L^2(\Omega)^2$ for the Stokes problem in a domain $\Omega,$ when $\Omega$
is a smooth domain or a convex polygon. We establish also a trace theorem and
show that the trace of $u$ can be arbitrary in $L^2(\partial\Omega)^2.$ The
results are also extended to the linear evolution Stokes problem.
