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In this expository note we discuss our recent work [arXiv:1306.5028] on thenonlinear asymptotic stability of shear flows in the 2D Euler equations ofideal, incompressible flow. In that work it is proved that perturbations to theCouette flow which are small in a suitable regularity class converge stronglyin $L^2$ to a shear flow which is close to the Couette flow. Enstrophy is mixedto small scales by an almost linear evolution and is generally lost in the weaklimit as t -> +/- infinity. In this note we discuss the most important physicaland mathematical aspects of the result and the key ideas of the proof.

Asymptotic stability for the Couette flow in the 2D Euler equations