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

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.