Self-organized hydrodynamic model with density-dependent velocity: local well-posedness and the limit from self-organized kinetic model

In this paper, we study the self-organized hydrodynamic (SOH) model with density-dependent velocity. This model was derived by Degond–Henkes–Yu (Kinet Relat Models 10(1):193-213, 2017). We prove the local well-posedness of the SOH model by energy method. From this well-posedness result we apply generalized collision invariants (GCIs) hypothesis and Hilbert expansion method to deduce the local existence of solutions for the scaled self-organized kinetic (SOK) equations. The main ingredient of this paper is that the SOH model is the macroscopic limit of the SOK equations as \(\epsilon \rightarrow 0\) $ϵ\to 0$ .