A justification on hydrodynamic limit for self-organized kinetic model with density-dependent parameters

In this paper, we justify the hydrodynamic limit of the self-organized kinetic (SOK) model with density-dependent parameters. Amic Frouvelle [10] derived this SOK model and formally deduced its hydrodynamic limit to get a self-organized hydrodynamic (SOH) model. Firstly, the local existence of the classical solution of the SOH equations is proved. Then we use Hilbert expansion method and generalized collision invariants (GCIs) hypothesis to construct the solutions of the SOK equations. Finally, we verify that the equilibrium related to the solution of the SOH equations is the limit of solutions of the SOK equations as ϵ→0.