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The asymptotic stability of two-dimensional stationary flows in anon-symmetric exterior domain is considered. Under the smallness condition oninitial perturbations, we show the stability of the small stationary flow whoseleading profile at spatial infinity is given by the rotating flow decaying inthe scale-critical order $O(|x|^{-1})$. Especially, we prove the $L^p$-$L^q$estimates to the semigroup associated with the linearized equations.

Note on the stability of planar stationary flows in an exterior domain without symmetry