On the global classical solution to compressible Euler system with singular velocity alignment

Abstract: We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establish a local well-posedness theory for the system, as well as a global well-posedness theory for small initial data. We also show the asymptotic flocking behavior, where solutions converge to a constant steady state exponentially in time.