2024-03-29T10:17:21Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698372022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Uniform exponential stability of the Ekman spiralGIGA, YOSHIKAZUJurgen, SaalStabilityvector-valued Radon measuresnondecaying functionsoperator-valued multipliersrotating boundary layersuniform well-posednessEkman layer410This paper studies stability of the Ekman boundary layer. We utilize a new approach developed by the authors in [12] 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 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. 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, H¨older or Besov spaces.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69837info:doi/10.14943/84177https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69837/1/pre1033.pdfHokkaido University Preprint Series in Mathematics10332172013-04-19engpublisher