The study of Stokes problem with time variable flux appears very interesting both from the physical and analytical points of view. In particular, what makes peculiar our results is the fact that we deduce estimates uniform with respect to the time, without assumptions of time integrability on the data F for Stokes problem and on the flux f(t) for Stokes problem. Moreover, in the latter cases the compatibility condition between the initial data v_0 and the flux f(t) in t=0, that is f(0), is studied without constrain for the behavior of the initial data. These aspects make the results of special interest as in the case of time periodic solutions or as in the case of the steady solutions as limit of unsteady solutions.