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On nontraditional quasi-geostrophic equations. (English) Zbl 1364.35280

Summary: In this article, we work on nontraditional models where the so-called traditional approximation on the Coriolis force is removed. In the derivation of the quasi-geostrophic equations, we carefully consider terms in \(\delta/\epsilon\), where \(\delta\) (aspect ratio) and \(\epsilon\) (Rossby number) are both small numbers. We provide here some rigorous crossed-asymptotics with regards to these parameters, prove some mathematical results and compare quasi-hydrostatic quasi-geostrophic (QHQG) and QG models.

MSC:

35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
86A05 Hydrology, hydrography, oceanography
35Q86 PDEs in connection with geophysics
76B65 Rossby waves (MSC2010)
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