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
DOI: 10.12677/aam.2025.142057, PDF,    科研立项经费支持
作者: 范芝瑶, 蒲志林*：四川师范大学数学科学学院，四川 成都
关键词: 非局部Cahn-Hilliard-Navier-Stokes系统；弱解；全局吸引子；Nonlocal Cahn-Hilliard-Navier-Stokes System； Weak Solution； Global Attractor
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。
Abstract: 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.
文章引用：范芝瑶, 蒲志林. 非局部Cahn-Hilliard-Navier-Stokes系统解的适定性和渐近行为[J]. 应用数学进展, 2025, 14(2): 109-124. https://doi.org/10.12677/aam.2025.142057

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