Cahn-Hilliard-Navier-Stokes方程的长时间行为  

Large Time Behavior of Cahn-Hilliard-Navier-Stokes Equations

作　　者：邝雪松 KUANG Xuesong(School of Mathematics and Computer,Guangdong Ocean University,Zhanjiang Guangdong 524088,China)

机构地区：[1]广东海洋大学数学与计算机学院,广东湛江524088

出　　处：《重庆师范大学学报（自然科学版）》2023年第2期96-102,共7页Journal of Chongqing Normal University:Natural Science

基　　金：广东省教育厅项目(No.570220005)。

摘　　要：[目的]Cahn-Hilliard-Navier-Stokes方程是由不可压缩的Navier-Stokes方程和高阶各项异性Cahn-Hilliard方程耦合而成,具有广泛应用和重要作用。[方法]通过能量估计得到方程的解半群存在有界吸收集和一致紧性。[结果]利用吸引子存在性定理验证了整体吸引子的存在性。[结论]研究了该方程在相对浓度满足Neumann边界条件下的长时间行为。[Purposes]The Cahn-Hilliard-Navier-Stokes equations,which are coupled by incompressible Navier-Stokes equations and higher-order anisotropic Cahn-Hilliard equations,are widely used and play an important role.[Methods]Bounded absorbing sets and uniform compactness of solution semigroup to the equations are obtained by using energy estimates.[FindingsJThen the existence of attractors are proved according to the existence theorem of attractor.[Conclusions]The large time behavior of the equations under Neumann boundary condition for relative concentrations is studied.

关 键 词：Cahn-Hilliard-Navier-Stokes方程 NEUMANN边界条件 吸收集 整体吸引子 

分 类 号：O175.29[理学—数学]