### 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} (ℝ^{2}; 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}(ℝ^{n}; E) for a general Banach space E.

Original language | English (US) |
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Pages (from-to) | 177-224 |

Number of pages | 48 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 186 |

Issue number | 2 |

DOIs | |

State | Published - Nov 1 2007 |

### ASJC Scopus subject areas

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

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_{+}

^{3}with initial data nondecreasing at infinity: The Ekman boundary layer problem.

*Archive for Rational Mechanics and Analysis*,

*186*(2), 177-224. https://doi.org/10.1007/s00205-007-0053-9