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Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity. (English) Zbl 1387.35469

Summary: We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero horizontal average and the space domain may be resonant. No smallness assumption is assumed on the initial data.

MSC:

35Q30 Navier-Stokes equations
76U05 General theory of rotating fluids
76B60 Atmospheric waves (MSC2010)
35Q86 PDEs in connection with geophysics
86A10 Meteorology and atmospheric physics
76B65 Rossby waves (MSC2010)
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