Improved estimates for the sharp interface limit of the stochastic Cahn–Hilliard equation with space-time white noise
Ľubomír Baňas
Bielefeld University, Bielefeld, GermanyJean Daniel Mukam
Bielefeld University, Bielefeld, Germany
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Abstract
We study the sharp interface limit of the stochastic Cahn–Hilliard equation with cubic double-well potential and additive space-time white noise , where is an interfacial width parameter. We prove that, for a sufficiently large scaling constant , the stochastic Cahn–Hilliard equation converges to the deterministic Mullins–Sekerka/Hele-Shaw problem for . The convergence is shown in suitable fractional Sobolev norms as well as in the -norm for in spatial dimension . This generalizes the existing result for the space-time white noise to dimension and improves the existing results for smooth noise, which were so far limited to in spatial dimension . As a byproduct of the analysis of the stochastic problem with space-time white noise, we identify minimal regularity requirements on the noise which allow convergence to the sharp interface limit in the -norm and also provide improved convergence estimates for the sharp interface limit of the deterministic problem.
Cite this article
Ľubomír Baňas, Jean Daniel Mukam, Improved estimates for the sharp interface limit of the stochastic Cahn–Hilliard equation with space-time white noise. Interfaces Free Bound. (2024), published online first
DOI 10.4171/IFB/518