A nonlocal stochastic Cahn-Hilliard equation

TL;DR

This paper studies a stochastic version of the nonlocal convective Cahn-Hilliard equation with additive noise, establishing the existence and uniqueness of solutions within a rigorous mathematical framework.

Contribution

It introduces a mathematical framework for a stochastic nonlocal Cahn-Hilliard equation and proves existence and uniqueness of solutions.

Findings

Existence of a weak statistical solution.

Existence and uniqueness of a strong solution.

Abstract

We consider a stochastic extension of the nonlocal convective Cahn-Hilliard equation containing an additive Wiener process noise. We first introduce a suitable analytical setting and make some mathematical and physical assumptions. We then establish, in a variational context, the existence of a weak statistical solution for this problem. Finally we prove existence and uniqueness of a strong solution.