Abstract

In my talk I will present some recent advances in the study of particular solutions of kinetic equations related to swarming and focus on a frequently used second-order self-propelled interacting particle system. It is well known that, in the mean-field limit of the particle systems, particular solutions such as flocks and rotating mills approach compactly supported continuous solutions of the associated kinetic equation. The explicit shape of spatial profiles of such solutions is generally unknown, as is existence and uniqueness for general interaction potentials. I will first discuss results on one particular class of potentials, so-called Quasi-Morse potentials, where explicit profiles and some uniqueness results can be established. Secondly, I will present a result on the stability of flock solutions in the second-order model for general potentials, which is given on the particle level.