Metastability of Kolmogorov flows
摘要: We study the metastability of the shear flow sin y (Kolmogorov flow) for 2D Navier-Stokes equation in 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 L2, 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.