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.
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Stefano Scrobogna, Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity. Rev. Mat. Iberoam. 34 (2018), no. 1, pp. 1–58DOI 10.4171/RMI/980