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Mathematische Annalen, 1989 The purpose of this paper is to verify the existence, uniqueness, and asymptotic behaviours of global strong solutions of the exterior nonstationary problem for the Navier-Stokes equation in \(L_ q\) spaces. The \(L_ q-L_ r\) estimates for the semigroup \(e^{-tA}\) generated by the Stokes operator in an exterior domain \(\Omega \subset {\mathbb{R}}^ n\)
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