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April 2015 Uniform exponential stability of the Ekman spiral
Yoshikazu Giga, Jürgen Saal
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Ark. Mat. 53(1): 105-126 (April 2015). DOI: 10.1007/s11512-014-0203-x

Abstract

This paper studies stability of the Ekman boundary layer. We utilize a new approach, developed by the authors in a precedent paper, based on Fourier transformed finite vector Radon measures, which yields exponential stability of the Ekman spiral. By this method we can also derive very explicit bounds for solutions of the linearized and the nonlinear Ekman systems. For example, we can prove these bounds to be uniform with respect to the angular velocity of rotation, which has proved to be relevant for several aspects. Another advantage of this approach is that we obtain well-posedness in classes containing nondecaying vector fields such as almost periodic functions. These outcomes give respect to the nature of boundary layer problems and cannot be obtained by approaches in standard function spaces such as Lebesgue, Bessel-potential, Hölder or Besov spaces.

Funding Statement

The work of the first author was partly supported by the Japan Society for the Promotion of Science through grant Kiban S (26220702), Kiban A (23244015) and Houga (25610025). This work was partly supported by the Japan Society for the Promotion of Science and the German Research Foundation through Japanese–German Graduate Externship and IRTG 1529.

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Yoshikazu Giga. Jürgen Saal. "Uniform exponential stability of the Ekman spiral." Ark. Mat. 53 (1) 105 - 126, April 2015. https://doi.org/10.1007/s11512-014-0203-x

Information

Received: 14 May 2013; Published: April 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1314.35101
MathSciNet: MR3319616
Digital Object Identifier: 10.1007/s11512-014-0203-x

Rights: 2014 © Institut Mittag-Leffler

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Vol.53 • No. 1 • April 2015
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