Pressureless Euler-Poisson equations with nonlocal forces

par Ewelina Zatorska (University College London)

jeudi 8 nov. 2018, 14:00 → 15:00 Europe/Paris

Salle de Séminaires (Orléans)

I will discuss the one-dimensional pressureless Euler-Poisson equations with a linear damping and non-local interaction forces. These equations are relevant for modelling  collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an explicit form of solution in Lagrangian coordinates which enables us to study the time-asymptotic behavior of classical solutions with the initial data in the subcritical region. 

This talk is based on the joint work with Jose Antonio Carrillo, Young-Pil Choi and Aneta Wroblewska-Kaminska.