Abstract
The semigeostrophic equations are a simple model used in meteorology to describe large scale atmospheric flows. As explained for instance in [31, Section 2.2] and [107, Section 1.1] (see also [68] for a more complete exposition), the semigeostrophic equations can be derived from the 3-d incompressible Euler equations, with Boussinesq and hydrostatic approximations, subject to a strong Coriolis force. Since for large scale atmospheric flows the Coriolis force dominates the advection term, the flow is mostly bi-dimensional. For this reason, the study of the semigeostrophic equations in 2-d or 3-d is pretty similar, and in order to simplify the presentation we focus here on the 2-dimensional periodic case, though the results have been extended to three dimensions and can be found in [8].
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