Stochastic Cahn-Hilliard equation in higher space dimensions: The motion\n of bubbles

2019/08/05 by Alexander Schindler, Schindler, Alexander, Dirk Blömker +1
Computer Science · Economics, Econometrics and Finance · Materials Science · Mathematics · Physics and Astronomy · #60H10 #60H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Solidification and crystal growth phenomena #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1908.01601

openalex publication_date 2019/08/05 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We study the stochastic motion of a droplet in a stochastic Cahn-Hilliard\nequation in the sharp interface limit for sufficiently small noise. The key\ningredient in the proof is a deterministic slow manifold, where we show its\nstability for long times under small stochastic perturbations. We also give a\nrigorous stochastic differential equation for the motion of the center of the\ndroplet.\n

Citations

• Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation

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