Dynamics for Generalized Incompressible Navier-Stokes Equations in R2

作者：Guo, Boling; Huang, Daiwen; Li, Qiaoxin; Sun, Chunyou^*

来源：Advanced Nonlinear Studies, 2016, 16(2): 249-272.

DOI：10.1515/ans-2015-5018

• Generalized Navier-Stokes Equation
• Inviscid Limit
• Global Attractor

In this paper, we consider the dynamics for damped generalized incompressible Navier-Stokes equations defined on R-2. The generalized Navier-Stokes equations here refer to the equations obtained by replacing the Laplacian in the classical Navier-Stokes equations by the more general operator (-Delta)(alpha) with alpha is an element of (1/2, 1). We prove that the rate of dissipation of enstrophy vanishes as nu -> 0(+), where nu is the viscosity parameter. Moreover, we prove the existence and finite dimensionality of a global attractor in (H-1(R-2))(2) as nu > 0 is kept fixed for the generalized Navier-Stokes equations.

• 出版日期2016-5
• 单位兰州大学; 北京应用物理与计算数学研究所