非局部Cahn-Hilliard-Navier-Stokes系统解的适定性和渐近行为  

Well-Posedness and Asymptotic Behavior of Solutions for Nonlocal Cahn-Hilliard-Navier-Stokes System

作　　者：范芝瑶 蒲志林 

机构地区：[1]四川师范大学数学科学学院,四川 成都

出　　处：《应用数学进展》2025年第2期109-124,共16页Advances in Applied Mathematics

基　　金：本文受到四川省科技厅科学研究基金(No.22CXTD0029)的资助。

摘　　要：文章主要研究在二维空间中非局部Cahn-Hilliard-Navier-Stokes系统弱解的适定性和长时间渐近行为。我们用标准的Galerkin方法并结合解的估计方法证明了弱解的整体存在性和唯一性,通过系统的能量方程得到了解的耗散估计,从而在空间m中建立了全局吸引子的存在性。This article mainly studies the well-posedness and long-term asymptotic behavior of the weak solution of nonlocal Cahn-Hilliard-Navier-Stokes system in two-dimensional space . We prove the global existence and uniqueness of weak solutions using the standard Galerkin method combined with the estimation method of solutions. We obtain the dissipative estimate of the solution through the energy equation of the system, and the existence of global attractors is established in m.

关 键 词：非局部Cahn-Hilliard-Navier-Stokes系统 弱解 全局吸引子 

分 类 号：O17[理学—数学]