Uniform Inviscid Damping and Inviscid Limit of 2D Navier-Stokes with Navier Boundary Conditions

Abstract: We present a series of works, joint with J. Bedrossian, S. He, F. Wang, in which we prove nonlinear inviscid damping, enhanced dissipation, and inviscid limit for the 2D Navier-Stokes equations near Couette. The domain is the periodic channel, \mathbb{T} \times [-1,1], and Navier Boundary Conditions are prescribed vertically. We will also make remarks about recent progress towards the no-slip case.