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We develop a global wellposedness theory for weak solutions to the 1DEuler-alignment system with measure-valued density, bounded velocity, andlocally integrable communication protocol. A satisfactory understanding of thelow-regularity theory is an issue of pressing interest, as smooth solutions maylose regularity in finite time. However, no such theory currently exists exceptfor a very special class of alignment interactions. We show that the dynamicsof the 1D Euler-alignment system can be effectively described by a nonlocalscalar balance law, the entropy conditions of which serves as an entropicselection principle that determines a unique weak solution of theEuler-alignment system. Moreover, the distinguished weak solution of the systemcan be approximated by the sticky particle Cucker--Smale dynamics. Our approachis inspired by the work of Brenier and Grenier [SIAM J. Numer. Anal,35(6):2317-2328, 1998] on the pressureless Euler equations.

Sticky particle Cucker-Smale dynamics and the entropic selection principle for the 1D Euler-alignment system