Transport phenomena in collective dynamics: from micro to social hydrodynamics

Hydrodynamic Models with Attractive-Repulsive and Alignment Effects

José Carrillo

Imperial College London

I will discuss several recent results regarding qualitative properties of hydrodynamic models with attractive-repulsive interactions. These models appear as natural monokinetic closures or hydrodynamic solutions of kinetic models for collective behavior. We will discuss critical thresholds and long time asymptotics for 1D models with alignment with/without interaction forces. In the pure alignment case and in the pure Euler-Poisson with confinement we will give sharp result distinguishing global existence and finite time blow-up with a complete understanding of the long time asymptotics. This is a summary of results based on works in collaboration with Y.-P. Choi, E. Tadmor, and C. Tan and with Y.-P. Choi and E. Zatorska.