I will present our recent work on linear and nonlinear stability of shear flows and vortices among solutions of the Euler equations in two dimensions. Our main results concern nonlinear asymptotic stability of a large class of monotonic shear flows in the finite channel, nonlinear asymptotic stability of point vortices in the plane, and linear stability of smooth decreasing vortices in the plane. This is joint work with Hao Jia.
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