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We consider the linearized 2-D Navier-Stokes equations around the Kolmogorov flow on the torus. Due to the vorticity mixing induced by the Kolmogorov flow, the decay rate of the solution is much faster than the diffusion decay rate. This phenomenon is so called enhanced dissipation, which plays an important role in the hydrodynamic stability. In this talk, I will introduce three methods (i.e., hypocoercivity method, wave operator method and resolvent estimate method) to establish the enhanced dissipation estimate for the Kolmogorov flow. If the time is permitted, I will also introduce our recent result about the linear inviscid damping and enhanced dissipation for monotone shear flows via the compactness method.

Note the delayed starting time, to accommodate the speaker.