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Well-posedness is proved for the stochastic viscous Cahn-Hilliard equationwith homogeneous Neumann boundary conditions and Wiener multiplicative noise.The double-well potential is allowed to have any growth at infinity (inparticular, also super-polynomial) provided that it is everywhere defined onthe real line. A vanishing viscosity argument is carried out and theconvergence of the solutions to the ones of the pure Cahn-Hilliard equation isshown. Some refined regularity results are also deduced for both the viscousand the non-viscous case.

The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit