  The superfluid phase transition of bosons in a two-dimensional (2D) system
with disorder and an external parabolic potential is studied. The theory is
applied to experiments on indirect excitons in coupled quantum wells. The
random field is allowed to be large compared to the dipole-dipole repulsion
between excitons. The slope of the external parabolic trap is assumed to change
slowly enough to apply the local density approximation (LDA) for the superfluid
density, which allows us to calculate the Kosterlitz-Thouless temperature
$T_{c}(n(r))$ at each local point $r$ of the trap. The superfluid phase occurs
around the center of the trap ($\mathbf{r}=0$) with the normal phase outside
this area. As temperature increases, the superfluid area shrinks and disappears
at temperature $T_{c}(n(r=0))$. Disorder acts to deplete the condensate; the
minimal total number of excitons for which superfluidity exists increases with
disorder at fixed temperature. If the disorder is large enough, it can destroy
the superfluid entirely. The effect of magnetic field is also calculated for
the case of indirect excitons. In a strong magnetic field $H$, the superfluid
component decreases, primarily due to the change of the exciton effective mass.
