Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

  title={Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations},
  author={J. Carrillo and M. DiFrancesco and A. Figalli and T. Laurent and D. Slep{\vc}ev},
  journal={Duke Mathematical Journal},
In this paper we provide a well-posedness theory for weak measure solutions of the Cauchy problem for a family of nonlocal interaction equations. These equations are continuum models for interacting particle systems with attractive/repulsive pairwise interaction potentials. The main phenomenon of interest is that, even with smooth initial data, the solutions can concentrate mass in finite time. We develop an existence theory that enables one to go beyond the blow-up time in classical norms and… Expand
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