Abstract
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.
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Research supported in part by NSFC (No.11671035). Financial support by the DFG through the CRC 1283 “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications” is acknowledged.
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Baňas, Ľ., Yang, H. & Zhu, R. Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise. Potential Anal 59, 497–518 (2023). https://doi.org/10.1007/s11118-021-09976-3
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DOI: https://doi.org/10.1007/s11118-021-09976-3
Keywords
- Stochastic Cahn-Hilliard equation
- Singular noise
- Sharp interface limit
- Mullins-Sekerka/Hele-Shaw problem