Prof. Eitan Tadmor, Ph.D.
Starting with agent-based descriptions, different models of large crowds flocking dynamics lead to hydrodynamic descriptions which involve alignment around non-local means. The global behavior of the resulting flocking hydrodynamics is dictated by the balance between nonlinear convection and these alignment forcing. In particular, there is a sharp dichotomy between the existences of global smooth solutions vs. finite-time blowup of strong solutions. This dichotomy is quantified in terms of critical thresholds (CT) in the space of initial configurations. We demonstrate this CT phenomena with several n-dimensional prototype models. These include prolonged life-span of sub-critical 2D shallow-water solutions, 3D restricted Euler and Euler-Poisson equations, and the hydrodynamic descriptions of flocking hydrodynamics.
Datum: 08.09.2016, Raum: G05-205 (Senatssaal), Zeit: 16:30