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BV Solutions to a Hydrodynamic Limit of Flocking Type

May 18, 2021
Abstract
Mathematical models introduced to capture the emergent behavior of self-organized systems have brought new challenges in the mathematical community and a lot of attention in the recent years. Most studies on flocking models have been on the behavior of the particle model or the corresponding kinetic formulation and its hydrodynamic formulation that provides in the limit an Euler-type flocking system. This area has been investigated so far in the context of smooth solutions. In this talk, we will discuss a hydrodynamic model of flocking type in the setting of entropy weak solutions. We (i) establish global existence of entropy weak solutions for arbitrary initial data of bounded variation with finite mass confined in a bounded interval and uniformly positive density therein and (ii) show that the entropy solution admits time asymptotic flocking. This is a joint work with Debora Amadori from University of L’Aquila.
Supplementary Materials