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

Local existence and uniqueness for a two-dimensional surface growth equation with space--time white noise