Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity

Scrobogna, Stefano

doi:10.4171/RMI/980

Revista Matemática Iberoamericana

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Volume 34, Issue 1, 2018, pp. 1–58

DOI: 10.4171/RMI/980

Published online: 2018-02-06

Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity

Stefano Scrobogna^[1]

(1) BCAM - Basque Center for Applied Mathematics, Bilbao, Spain and Université de Bordeaux, France

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.

Keywords: Stratified fluids, rotating fluids, Schochet method, dispersion

Scrobogna Stefano: Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity. Rev. Mat. Iberoamericana 34 (2018), 1-58. doi: 10.4171/RMI/980