Abstract
This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕα(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)=ργ, γ=1+2d from that kinetic equation.
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