Stability of a two‐dimensional stationary rotating flow in an exterior cylinder

We investigate the stability of an exact stationary flow in an exterior cylinder. The horizontal velocity is the two‐dimensional rotating flow in an exterior disk with a critical spatial decay, for which the L2 stability is known under smallness conditions. We prove its stability property for three‐dimensional perturbations although the Hardy type inequalities are absent as in the two‐dimensional case. The proof uses a large time estimate for the linearized equations exhibiting different behaviors in the Fourier modes, namely, the standard L2‐Lq$L^q$ decay of the two‐dimensional mode and an exponential decay of the three‐dimensional modes.