Explicit equilibrium solutions for the aggregation equation with power-law potentials - Carrillo, JA; Huang, Y (American Institute of Mathematical Sciences, 2017)
Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions of the aggregation equation with power-law kernelsare constructed by inverting Fredholm integral operators or byemploying certain integral identities. These solutions are expected tobe the global energy stable equilibria and to characterize the generic behaviorsof stationary solutions for more general interactions.