On circular flows: Linear stability and damping

In this article we establish linear inviscid damping with optimal decay rates around 2D Taylor-Couette flow and similar monotone flows in an annular domain B_r2 (0) ∖B_r1 (0) ⊂R². Following recent results by Wei, Zhang and Zhao [10], we establish stability in weighted norms, which allow for a singularity formation at the boundary, and additionally provide a description of the blow-up behavior.