  Different approaches to the nonlinear dynamics of premixed flames exist in
the literature: equations based on developments in a gas ex- pansion parameter,
weak nonlinearity approximation, potential model equation in a coordinate-free
form. However the relation between these different equations is often unclear.
Starting here with the low vor- ticity approximation proposed recently by one
of the authors, we are able to recover from this formulation the dynamical
equations usually obtained at the lowest orders in gas expansion for plane on
average flames, as well as obtain a new second order coordinate-free equation
extending the potential flow model known as the Frankel equation. It is also
common to modify gas expansion theories into phenomelogical equations, which
agree quantitatively better with numerical simula- tions. We discuss here what
are the restrictions imposed by the gas expansion development results on this
process.
