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Existence of solutions to the nonstationary Stokes system in H-μ2,1, μ∈(0,1), in a domain with a distinguished axis. Part 2. Estimate in the 3d case

2007
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Applicationes Mathematicae
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EXISTENCE OF SOLUTIONS TO THE NONSTATIONARY STOKES SYSTEM IN H 2,1 −µ , µ ∈ (0, 1), IN A DOMAIN WITH A DISTINGUISHED AXIS. PART 2. ESTIMATE IN THE 3d CASE Abstract. We examine the regularity of solutions to the Stokes system in a neighbourhood of the distinguished axis under the assumptions that the initial velocity v 0 and the external force f belong to some weighted Sobolev spaces. It is assumed that the weight is the (−µ)th power of the distance to the axis. Let f ∈ L 2,−µ , v 0 ∈ H 1 −µ , µ

doi:10.4064/am34-2-2
fatcat:tuksbqfxxbbonh4u7ehow2p3qq