Existence and ergodicity for the two-dimensional stochastic Allen-Cahn-Navier-Stokes equations

被引：0

作者：

Ngana, Aristide Ndongmo ^{[1
,2
]}

Medjo, Theodore Tachim ^{[3
]}

机构：

[1] Univ Dschang, Dept Math & Comp Sci, POB 67, Dschang, Cameroon

[2] North West Univ, Sch Math & Stat Sci, Potchefstroom, South Africa

[3] Florida Int Univ, Dept Math & Stat, MMC, Miami, FL 33199 USA

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2024年 / 43卷 / 1-2期

关键词：

stochastic; Allen-Cahn; Navier-Stokes equations; invariant measure; coupling; ergodicity; BOUSSINESQ EQUATIONS; UNIQUE STRONG; ATTRACTORS; MODEL;

D O I：

10.4171/ZAA/1752

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study in this article a stochastic version of a coupled Allen-Cahn-Navier-Stokes model in a two-dimensional bounded domain. The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter, both endowed with suitable boundary conditions. We prove the existence of solutions via a semigroup approach. We also obtain the existence and uniqueness of an invariant measure via coupling methods.

引用

页码：1 / 48

页数：48

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