  We describe the three-body loss coefficient of identical fermions with
$p$-wave interactions using a set of rate equations in which three-body
recombination happens via an indirect process. Our theoretical treatment
explains experimental results just above the universal scaling law regime of
weak interactions. Furthermore, we theoretically extend and experimentally
verify the rate equation model for the case of atoms trapped in two dimensions.
Moreover, we find that the three-body loss coefficient in a two-dimensional
trap is proportional to $A_{p}^{3}$ in the weakly interacting regime, where
$A_{p}$ is the scattering area. Our results are useful in understanding
three-body physics with $p$-wave interactions.
