This survey summarizes and illustrates the main qualitative properties of hydrodynamics
models for collective behavior. These models include a velocity consensus term together …

These notes are devoted to a summary on the mean-field limit of large ensembles of
interacting particles with applications in swarming models. We first make a summary of the …

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 …

We consider the multidimensional aggregation equation ut−∇·(u∇ K* u)= 0 in which the
radially symmetric attractive interaction kernel has a mild singularity at the origin (Lipschitz …

In this work we consider local minimizers (in the topology of transport distances) of the
interaction energy associated with a repulsive–attractive potential. We show how the …

We consider the aggregation equation ρ t−∇·(ρ∇ K* ρ)= 0 in, where the interaction potential
K models short-range repulsion and long-range attraction. We study a family of interaction …

We consider well‐posedness of the aggregation equation∂ tu+ div (uv)= 0, v=−▿ K* u with
initial data in\input amssym \calP_2\rm(\BbbR^d\rm)∩L^p(\BbbR^d) in dimensions 2 and …

Recently, there has been a wide interest in the study of aggregation equations and Patlak–
Keller–Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper …

Nonlocal advection is a key process in a range of biological systems, from cells within
individuals to the movement of whole organisms. Consequently, in recent years, there has …

We study equilibrium configurations of swarming biological organisms subject to exogenous
and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a …