Rotating Navier-Stokes equations in ℝ+3 with initial data nondecreasing at infinity: The Ekman boundary layer problem

Yoshikazu Giga, Katsuya Inui, Alex Mahalov, Shin'ya Matsui, Jürgen Saal

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)177-224
Number of pages48
JournalArchive for Rational Mechanics and Analysis
Volume186
Issue number2
DOIs
StatePublished - Nov 1 2007

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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