From BGK-alignment model to the pressured Euler-alignment system with singular communication weights.

This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕ α (x) = | x | − α for some α > 0. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from the BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure p (ρ) = ρ γ , γ = 1 + 2 d from that kinetic equation. [ABSTRACT FROM AUTHOR]