# Inviscid damping near Couette flow in a channel

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Hao Jia, University of Minnesota
Fine Hall 314

An important feature for two dimensional Euler equation is the mixing of the vorticity. The mixing averages" the vorticity and can sometimes drive the flow towards an equilibrium. In a breakthrough work, Bedrossian and Masmoudi established this mechanism (inviscid damping) in a Gevrey neighborhood of Couette flow in the whole space. As an attempt to understand their work, we consider the inviscid damping near Couette flow in a periodic channel, when the perturbed vorticity is supported away from the boundary. We show that the inviscid damping takes place in this case as well, in a sharper space. Difficulty with extending such results to general shear flow and general boundary effects will also be briefly discussed. This is based on joint work with Alex Ionescu.