Weak Solutions with Bounded Support to an Euler-Type Flocking Model

We give an overview of the recents results obtained in [1] on the existence and time-asymptotic flocking of weak solutions to a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension. An appropriate notion of entropy weak solutions with bounded support is described, to capture the behavior of solutions to the Cauchy problem with any BV initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein. In addition, a suitable condition on the initial data is provided that allows us to show time-asymptotic flocking for such solutions.