On the Rate of Decay of the Oseen Semigroup in Exterior Domains and its Application to Navier–Stokes Equation
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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.
Mathematics Subject Classification (2000).35B40 35M20 73B30
Keywords.Oseen semigroup Lp−Lq estimate exterior domain stability stationary solution
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