  Existence and uniqueness of solutions to the Navier-Stokes equation in
dimension two with forces in the space $L^q( (0,T); \mathbf{W}^{-1,p}(\Omega))$
for $p$ and $q$ in appropriate parameter ranges are proven. The case of
spatially measured-valued inhomogeneities is included. For the associated
Stokes equation the well-posedness results are verified in arbitrary dimensions
with $1 < p, q < \infty$ arbitrary.
