We prove L p -L q estimates of the Oseen semigroup in n-dimensional exterior domains $$(n\,\geqslant\, 3),$$ which refine and improve those obtained by Kobayashi and Shibata . As an application, we give a globally in time stability theory for the stationary Navier-Stokes flow whose velocity at infinity is a non-zero constant vector. We thus extend the result of Shibata . In particular, we find an optimal rate of convergence of solutions of the non-stationary problem to those of the corresponding stationary problem.
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