On the pressureless damped Euler-Poisson equations with non-local   forces: Critical thresholds and large-time behavior
  We analyse 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. 
Jos\'e A. Carrillo and Young-Pil Choi and Ewelina Zatorska
math.AP