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Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise

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arxiv 1905.07216 v2 pith:4K4ESFZD submitted 2019-05-17 math.PR math.AP

Lubomir Banas , Huanyu Yang and , Rongchan Zhu This is my paper · ORCID
classification math.PRmath.AP
keywords noiseequationlimitsolutionscahn-hilliardinterfacesharpstochastic
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abstract

We study the the sharp interface limit of $\varepsilon$-dependent two dimensional stochastic Cahn-Hilliard equation driven by space-time white noise and conservative noise as $\varepsilon\to 0$. In the case when the noise is sufficiently small, by comparing the solutions to equation (1.1) with the approximation solution constructed in [ABC94], we show that the limit of the solutions is also solutions to the deterministic Hele-Shaw problem.

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  1. Stochastic Cahn-Hilliard equation in higher space dimensions: The motion of bubbles

    math.DS 2019-08 conditional novelty 6.0 of 10

    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 essenti...

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