Orateur
Description
We study the collective dynamics of a population subject to self-consistent attraction-repulsion interactions and an external velocity field. We start form a Vlasov-like description of the population in the regime of strong interaction forces. We show that the population asymptotically concentrates within a domain $\Omega(t)=\Omega_0+X(t)$ whose shape $\Omega_0$ is determined by the minimization of the interaction energy while the evolution of the domain’s center of mass $X(t)$ is determined by the external force field.
In addition, we show that inside the domain the motion of the organisms is governed by the lake equation, a variant of the incompressible Euler system. The analysis uses variational approaches and modulated energy methods.