Degenerate SDEs in Hilbert spaces with rough drifts

The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and Hölder continuous of order larger than 2/3 in the other component. In the finite-dimensional case the Dini continuity is further weakened. The main results are applied to solve second order stochastic systems driven by spacetime white noises.