  In atmospheric science, slice models are frequently used to study the
behaviour of weather, and specifically the formation of atmospheric fronts,
whose prediction is fundamental in meteorology. In 2013, Cotter and Holm
introduced a new slice model, which they formulated using Hamilton's
variational principle, modified for this purpose. In this paper, we show the
local existence and uniqueness of strong solutions of the related ISM
(Incompressible Slice Model). The ISM is a modified version of the Cotter-Holm
Slice Model (CHSM) that we have obtained by adapting the Lagrangian function in
Hamilton's principle for CHSM to the Euler-Boussinesq Eady incompressible case.
Besides proving local existence and uniqueness, in this paper we also construct
a blow-up criterion for the ISM, and study Arnold's stability around a
restricted class of equilibrium solutions. These results establish the
potential applicability of the ISM equations in physically meaningful
situations.
