Abstract
In this paper, we prove the inviscid damping and vortex axisymmetrization for the linearized Euler equation around the radially symmetric, strictly monotonic vorticity distribution via the vector field method. One of the key ingredients is to establish the limiting absorption principle for the Rayleigh equation. Compared with shear flows in a channel, the main difficulty comes from the degeneration of the pipe flow at the original point and infinity.
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