Work

The stochastic nonlocal Cahn–Hilliard equation with regular potential and multiplicative noise

Year: 2026

Type: article

Abstract: In this work, we deal with the stochastic counterpart of the nonlocal Cahn-Hilliard equation with regular potential in a smooth bounded one-, two- or three-dimensional domain. The problem is endowed with homogeneous Neumann boundary conditions and random initial data. Furthermore, the system is driven by cylindrical noise of multiplicative type. For the resulting system, we are able to show the existence of probabilistically-weak (or martingale) solutions in two and three dimensions, that are unique and probabilistically-strong under suitable assumptions on the stochastic diffusion. Moreover, we investigate the nonlocal-to-local asymptotics toward solutions of the local stochastic Cahn-Hilliard equations, establishing, under regularity conditions, a precise rate of convergence as well.

Source: Stochastic Partial Differential Equations Analysis and Computations

DOI: 10.1007/s40072-026-00430-2

Authors: Andrea Di Primio, Christoph Hurm

Institutions: Scuola Normale Superiore, University of Regensburg

Language: English

Topic: Solidification and crystal growth phenomena

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Scuola Normale Superiore, Deutsche Forschungsgemeinschaft, European Research Council