Solving the Cahn-Hilliard equation with additive noise

TL;DR

This paper establishes the local well-posedness of the stochastic Cahn-Hilliard equation with additive noise using advanced mathematical techniques.

Contribution

It introduces a novel application of paracontrolled calculus and the Da Prato-Debussche trick to this equation.

Findings

Proved local well-posedness of the stochastic Cahn-Hilliard equation.

Applied paracontrolled calculus to handle noise.

Utilized the Da Prato-Debussche method for solution construction.

Abstract

We prove local well-posedness of the Cahn-Hilliard equation with additive noise. Our method relies on paracontrolled calculus and the Da Prato-Debussche trick.