Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains

Existence and uniqueness of solutions to the Navier-Stokes equations in dimension two with forces in the space Lq((0, T); W−1,p(Ω)) for p and q in appropriate parameter ranges are proven. The case of spatially measured-valued forces is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions for any 1 < p, q < ∞