  We present 2D hydrodynamic simulations of circumstellar disks around
protostars using a `Piecewise Parabolic Method' (PPM) code. We include a point
mass embedded within the disk and follow the migration of that point mass
through the disk. Companions with masses $M_c\ga 0.5M_J$ can open a gap in the
disk sufficient to halt rapid migration through the disk. Lower mass companions
open gaps, but migration continues because sufficient disk mass remains close
to the disk to exert large tidal torques. We find that the torques which
dominate the migration of low mass planets originate within a radial region
within 1-2 Hill radii of the planet's orbit radius, a distance smaller than the
thickness of the disk. We conclude that a very high resolution 3D treatment
will be required to adequately describe the planet's migration.
