  Fast pairwise conversions of neutrinos are predicted to be ubiquitous in
neutron star merger remnants with potentially major implications on the
nucleosynthesis of the elements heavier than iron. We present the first
sophisticated numerical solution of the neutrino flavor evolution above the
remnant disk within a (2+1+1) dimensional setup: two spatial coordinates, one
angular variable, and time. We look for a steady-state flavor configuration
above the remnant disk. Albeit the linear stability analysis predicts flavor
instabilities at any location above the remnant disk, our simulations in the
non-linear regime show that fast pairwise conversions lead to minimal neutrino
mixing (<1%); flavor equilibration is never achieved in our models.
Importantly, fast neutrino conversions are more prominent within localized
regions near the edges of the (anti)neutrino decoupling surfaces and almost
negligible in the polar region of the remnant. Our findings on the role of fast
pairwise conversions should be interpreted with caution because of the
approximations intrinsic to our setup and advocate for further work within a
more realistic framework.
