主题：Metastability of Kolmogorov flows and inviscid damping of shear flows
摘要：We study the metastability of the shear flow sin y (Kolmogorov
flow) for 2D Navier-Stokes equation on a torus. This flow is nonlinearly stable for the inviscid case. When the viscosity is small enough, it is shown that the non-shear part of the perturbations can decay at a much faster rate than the viscous time scale, for an intermediate but long time period. The result is true for the linearized NS equation with any initial vorticity in L^2, and for the nonlinear NS equation with initial vorticity of the size of viscosity. We also consider the inviscid damping for two classes of shear flows by using the Hamiltonian
structures of the linearized Euler equation. This is a joint work with Ming Xu.