二维Navier-Stokes-Cahn-Hilliard系统光滑解的全局存在性和L^(2)衰减估计  

Global Well-posedness and L^(2)-Decay Estimate of Smooth Solution for the 2-D Incompressible Navier-Stokes-Cahn-Hilliard System

作　　者：刘烨芳 滕凯民 LIU Yefang;TENG Kaimin(College of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China)

机构地区：[1]太原理工大学数学学院,山西晋中030600

出　　处：《应用数学》2023年第3期613-630,共18页Mathematica Applicata

基　　金：山西省自然科学基金面上项目(201901D111085)。

摘　　要：本文研究二维不可压缩Navier-Stokes-Cahn-Hilliard系统.假设初值(u_(0),φ_(0))∈H^(s)(R^(2))×H^(s)(R^(2))并且divu_(0)=0,其中s∈N且s> 1,通过利用能量估计的方法证明该系统存在唯一的全局光滑解.此外,采用Fourier分离方法,研究该系统光滑解及其高阶空间导数的L^(2)-衰减估计.In this paper,we study the 2-D incompressible Navier-Stokes-Cahn-Hilliard equations.The existence and uniqueness of global smooth solution is established under the assumptions of(u_0,φ_0) ∈H^(s)(R^(2)) × H^(s)(R^(2)) and div u_(0) = 0,where s ∈ N and s 1,through using the energy estimates approaches.Moreover,we show the large time behavior of smooth solution and its higher-order spatial derivatives by using the Fourier-splitting method.

关 键 词：Navier-Stokes-Cahn-Hilliard系统 Fourier分离方法 L^(2)衰减估计 

分 类 号：O175.24[理学—数学]