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

17 Citations (Scopus)

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,σ 0 (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∞,1 0 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 ∞,1 0(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 2007

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Besov Spaces
Navier Stokes equations
Boundary Layer
Rotating
Navier-Stokes Equations
Boundary layers
Infinity
Homogeneous Space
Banach spaces
Almost Periodic Functions
Local Existence
Existence and Uniqueness of Solutions
Stationary Solutions
Integrability
Calculus
Choose
Banach space
Decay
Operator

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Mathematics(all)
  • Mathematics (miscellaneous)

Cite this

Rotating Navier-Stokes equations in ℝ+ 3 with initial data nondecreasing at infinity : The Ekman boundary layer problem. / Giga, Yoshikazu; Inui, Katsuya; Mahalov, Alex; Matsui, Shin'ya; Saal, Jürgen.

In: Archive for Rational Mechanics and Analysis, Vol. 186, No. 2, 11.2007, p. 177-224.

Research output: Contribution to journalArticle

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