  We study local existence and uniqueness for a surface growth model with
space-time white noise in 2D. Unfortunately, the direct fixed-point argument
for mild solutions fails here, as we do not have sufficient regularity for the
stochastic forcing. Nevertheless, one can give a rigorous meaning to the
stochastic PDE and show uniqueness of solutions in that setting. Using spectral
Galerkin method and any other types of regularization of the noise, we obtain
always the same solution.
