For sufficiently small additive noise, a 2D droplet in the stochastic Cahn-Hilliard equation remains near the deterministic slow manifold for polynomial times, and its center satisfies a derived SDE with noise essentially the projection of the Wiener process onto the translational modes.
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Stochastic Cahn-Hilliard equation in higher space dimensions: The motion of bubbles
For sufficiently small additive noise, a 2D droplet in the stochastic Cahn-Hilliard equation remains near the deterministic slow manifold for polynomial times, and its center satisfies a derived SDE with noise essentially the projection of the Wiener process onto the translational modes.