Wong–Zakai approximation for a stochastic 2D Cahn–Hilliard–Navier–Stokes model

Pub Date : 2024-07-19 DOI:10.1002/mana.202400065
T. Tachim Medjo
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Abstract

In this paper, we demonstrate the Wong–Zakai approximation results for two dimensional stochastic Cahn–Hilliard–Navier–Stokes model. The model consists of a Navier–Stokes system coupled with convective Cahn–Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite-dimensional approximation of this process. Note that the coupling between the Navier–Stokes system and the Cahn–Hilliard equations makes the analysis more involved.

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随机二维 Cahn-Hilliard-Navier-Stokes 模型的 Wong-Zakai 近似值
本文展示了二维随机卡恩-希利亚德-纳维尔-斯托克斯模型的 Wong-Zakai 近似结果。该模型由与对流卡恩-希利亚德方程耦合的纳维-斯托克斯系统组成。它描述了两种(部分)不溶流体的不可压缩等温混合物在乘法噪声影响下的运动。我们的主要结果描述了解的分布支持。与文献[2]一样,这两个结论都是通过希尔伯特值布朗运动驱动的非线性随机 PDE 的概率收敛的一般 Wong-Zakai 型结果以及该过程的某些适应性有限维近似来证明的。需要注意的是,纳维-斯托克斯系统与卡恩-希利亚德方程之间的耦合使得分析更加复杂。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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