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

Hydrodynamic limit of a kinetic flocking model with nonlinear velocity alignment