Abstract
In this paper we develop a new approach to rotating boundary layers via Fourier transformed finite vector Radon measures. As an application we consider the Ekman boundary layer. By our methods we can derive very explicit bounds for existence intervals and solutions of the linearized and the nonlinear Ekman system. 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 (see introduction). Another advantage of our 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.
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Giga, Y., Saal, J. An Approach to Rotating Boundary Layers Based on Vector Radon Measures. J. Math. Fluid Mech. 15, 89–127 (2013). https://doi.org/10.1007/s00021-012-0094-1
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DOI: https://doi.org/10.1007/s00021-012-0094-1