  We consider the hydrodynamic limit of a collisionless and non-diffusive
kinetic equation under strong local alignment regime. The local alignment is
first considered by Karper, Mellet and Trivisa in [24], as a singular limit of
an alignment force proposed by Motsch and Tadmor in [32]. As the local
alignment strongly dominate, a weak solution to the kinetic equation under
consideration converges to the local equilibrium, which has the form of
mono-kinetic distribution. We use the relative entropy method and weak
compactness to rigorously justify the weak convergence of our kinetic equation
to the pressureless Euler system.
