Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

Banas L, Yang H, Zhu R. Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise. Potential Analysis . 2022.We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem