  We investigate the stability, with respect to spatial inhomogeneity, of a
two-dimensional dense neutrino gas. The system exhibits growth of seed
inhomogeneity due to nonlinear coherent neutrino self-interactions. In the
absence of incoherent collisional effects, we observe a dependence of this
instability growth rate on the neutrino mass spectrum: the normal neutrino mass
hierarchy exhibits spatial instability over a larger range of neutrino number
density compared to that of the inverted case. We further consider the effect
of elastic incoherent collisions of the neutrinos with a static background of
heavy, nucleon-like scatterers. At small scales, the growth of flavor
instability can be suppressed by collisions. At large length scales we find,
perhaps surprisingly, that for inverted neutrino mass hierarchy incoherent
collisions fail to suppress flavor instabilities, independent of the coupling
strength.
