Small Inertia Limit for Coupled Kinetic Swarming Models

We investigate various versions of multi-dimensional systems involving many species, modeling aggregation phenomena through nonlocal interaction terms. We establish a rigorous connection between kinetic and macroscopic descriptions by considering the small inertia limit at the kinetic level. The results are proved either under smoothness assumptions on all interaction kernels or under singular assumptions for self-interaction potentials. Utilizing different techniques in the two cases, we demonstrate the existence of a solution to the kinetic system, provide uniform estimates with respect to the inertia parameter, and show convergence toward the corresponding macroscopic system as the inertia approaches zero.