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# Rotating Navier-Stokes Equations in ${\mathbb R}^{3}_{+}$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem

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 Please use this identifier to cite or link to this item:https://doi.org/10.14943/83911

 Title: Rotating Navier-Stokes Equations in ${\mathbb R}^{3}_{+}$ with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem Authors: Giga, Y. Browse this author Inui, K. Browse this author Mahalov, A. Browse this author Matsui, S. Browse this author Saal, J. Browse this author Keywords: boundary layer problem Ekman spiral Rotating Navier-Stokes equations Stokes operator nondecreasing initial data vector-valued homoge-neous Besov spaces Mikhlin theorem Riesz operators operator-valued bounded H1-calculus. Issue Date: 2005 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 761 Start Page: 1 End Page: 49 Abstract: We prove time-local existence and uniqueness of solutions to a boundary layer roblem in a rotating frame around the stationary solution called Ekman spiral. Initial ata we choose in the vector-valued homogeneous Besov space _ B01 1; (R2;Lp(R+)) for < p < 1. Here the Lp-integrability is imposed in the normal direction, while we ay have no decay in tangential components, since the Besov space _ B01 1 contains ondecaying functions such as almost periodic functions. A crucial ingredient is theory or vector-valued homogeneous Besov spaces. For instance we provide and apply an perator-valued bounded H1-calculus for the Laplacian in _ B01 1(Rn; E) for a general anach space E. Type: bulletin (article) URI: http://hdl.handle.net/2115/69569 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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