Abstract
Based on theL p−Lq-estimates for the Stokes semigroup on exterior domains, proven by Iwashita and refined by Maremonti-Solonnikov and Shibata, the precise time-asymptotic behaviour of solutions of the Navier-Stokes equations is derived. The estimates are improved, if some additional information on the initial value is available. The results apply also to weak solutions in three and four dimensions.
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