  We investigate numerically and analytically the effects of hydrodynamics on
the dynamics of topological defects in $p-$atic liquid crystals, i.e.
two-dimensional liquid crystals with $p-$fold rotational symmetry. Importantly,
we find that hydrodynamics fuels a generic passive self-propulsion mechanism
for defects of winding number $s=(p-1)/p$ and arbitrary $p$. Strikingly, we
discover that hydrodynamics always accelerates the annihilation dynamics of
pairs of $\pm 1/p$ defects, and that, contrary to expectations, this effect
increases with $p$. Our Letter paves the way towards understanding cell
intercalation and other remodelling events in epithelial layers.
