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A Geometric Optics Type Approach to Fluid Boundary Layers

Abstract This note is devoted to the existence of rigorous asymptotic expansions for some boundary layer problems. We follow ideas of geometric optics and show that, generically, the study of such expansions is linked to the kernel and range of suitable projectors. We apply this remark to some classical geophysical systems, and recover in particular the results of (Grenier, E., Masmoudi, N. (1997). Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations 22(5–6):953–975) with some improvements.