Large deviations for a stochastic Cahn-Hilliard equation in Hölder norm

A nonlocal stochastic Cahn-Hilliard equation

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.

Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise

We study the the sharp interface limit of $\varepsilon$-dependent two dimensional stochastic Cahn-Hilliard equation driven by space-time white noise and conservative noise as $\varepsilon\to 0$. In the case when the noise is sufficiently small, by comparing the solutions to equation (1.1) with the approximation solution constructed in [ABC94], we show that the limit of the solutions is also solutions to the deterministic Hele-Shaw problem.

The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit

Well-posedness is proved for the stochastic viscous Cahn-Hilliard equation with homogeneous Neumann boundary conditions and Wiener multiplicative noise. The double-well potential is allowed to have any growth at infinity (in particular, also super-polynomial) provided that it is everywhere defined on the real line. A vanishing viscosity argument is carried out and the convergence of the solutions to the ones of the pure Cahn-Hilliard equation is shown. Some refined regularity results are also deduced for both the viscous and the non-viscous case.

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

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

关于随机Cahn-Hilliard-Brinkman模型

On a stochastic Cahn-Hilliard-Brinkman model

本文提出了一种随机Cahn-Hilliard-Brinkman模型，结合Brinkman方程与Cahn-Hilliard方程，通过随机噪声描述两相流，并证明了弱解的存在性。

随机Cahn-Hilliard方程的拟控方法

Paracontrolled approach to the stochastic Cahn-Hilliard equation

该研究针对空间维数1至5的随机Cahn-Hilliard方程，分别采用Da Prato-Debussche技巧（d=4）与拟控分布（d=5），证明了其局部时间解的存在性与唯一性。

Weak convergence of the backward Euler method for stochastic Cahn--Hilliard equation with additive noise

We prove a weak rate of convergence of a fully discrete scheme for stochastic Cahn--Hilliard equation with additive noise, where the spectral Galerkin method is used in space and the backward Euler method is used in time. Compared with the Allen--Cahn type stochastic partial differential equation, the error analysis here is much more sophisticated due to the presence of the unbounded operator in front of the nonlinear term. To address such issues, a novel and direct approach has been exploited which does not rely on a Kolmogorov equation but on the integration by parts formula from Malliavin c…