  In this paper we study a recently derived mathematical model for nonlinear
propagation of waves in the atmosphere, for which we establish the local
well-posedness in the setting of classical solutions. This is achieved by
formulating the model as a quasilinear parabolic evolution problem in an
appropriate functional analytic framework and by using abstract theory for such
problems. Moreover, for $L_2$-initial data, we construct global weak solutions
by employing a two-step approximation strategy based on a Galerkin scheme,
where an equivalent formulation of the problem in terms of a new variable is
used. Compared to the original model, the latter has the advantage that the
$L_2$-norm is a Liapunov functional.
