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We consider the compressible Euler system with a family of nonlinear velocityalignments. The system is a nonlinear extension of the Euler-alignment systemin collective dynamics. We show the asymptotic emergent phenomena of thesystem: alignment and flocking. Different types of nonlinearity and nonlocalcommunication protocols are investigated, resulting in a variety of differentasymptotic behaviors.

Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment