  We investigate a class of Vlasov-type kinetic flocking models featuring
nonlinear velocity alignment. Our primary objective is to rigorously derive the
hydrodynamic limit leading to the compressible Euler system with nonlinear
alignment. This study builds upon the work by Figalli and Kang [Anal. PDE,
12(3), 843-866, 2018], which addressed the scenario of linear velocity
alignment using the relative entropy method. The introduction of nonlinearity
gives rise to an additional discrepancy in the alignment term during the
limiting process. To effectively handle this discrepancy, we employ the
monokinetic ansatz in conjunction with the relative entropy approach.
Furthermore, our analysis reveals distinct nonlinear alignment behaviors
between the kinetic and hydrodynamic systems, particularly evident in the
isothermal regime.
