  We establish the local and global well-posedness of strong solutions to the
two- and three-dimensional anelastic equations of stratified viscous flows. In
this model, the interaction of the density profile with the velocity field is
taken into account, and the density background profile is permitted to have
physical vacuum singularity. The existing time of the solutions is infinite in
two dimensions, with general initial data, and in three dimensions with small
initial data.
