Consider the mass outflow (inflow?) of a single star, where the mass loss rate and flow velocity are both functions of time and latitude:

The evolution of the circumstellar gas is described by the Euler equations for an ideal, inviscid gas:

Together with the above boundary conditions at the stellar surface, and perhaps some radiative cooling, we have the ingredients for the GISW.

Here we have at most radiative cooling (G), and no forces (F). We neglect magnetic fields, conduction and photoionization effects, which are expected to be important in circumstellar environments.