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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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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
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

Submitter: 数学紀要登録作業用

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