Abstract: Existence and uniqueness of solutions to the Navier-Stokes equations in dimension two with forces in the space Lq((0; T);W??1;p( )) 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 veried in arbitrary dimensions for any 1 < p; q < 1.

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