TY - JOUR

T1 - Rotating Navier-Stokes equations in ℝ+3 with initial data nondecreasing at infinity

T2 - The Ekman boundary layer problem

AU - Giga, Yoshikazu

AU - Inui, Katsuya

AU - Mahalov, Alex

AU - Matsui, Shin'ya

AU - Saal, Jürgen

N1 - Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.

PY - 2007/11

Y1 - 2007/11

N2 - We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space Ḃ∞,1,σ0 (ℝ2; L p (ℝ+)) for 2 < p < ∞. Here the L p -integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space Ḃ∞,10 contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous Besov spaces. For instance we provide and apply an operator-valued bounded H ∞-calculus for the Laplacian in Ḃ ∞,10(ℝn; E) for a general Banach space E.

AB - We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space Ḃ∞,1,σ0 (ℝ2; L p (ℝ+)) for 2 < p < ∞. Here the L p -integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space Ḃ∞,10 contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous Besov spaces. For instance we provide and apply an operator-valued bounded H ∞-calculus for the Laplacian in Ḃ ∞,10(ℝn; E) for a general Banach space E.

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U2 - 10.1007/s00205-007-0053-9

DO - 10.1007/s00205-007-0053-9

M3 - Article

AN - SCOPUS:34848825320

VL - 186

SP - 177

EP - 224

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -