Sticky particle dynamics with interactions
  We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimension. We assume that the fluid self-interacts through a force field generated by the fluid itself. We explain how this flow can be described by a differential inclusion on the space of transport maps, in particular when a sticky particle dynamics is assumed. We study a discrete particle approximation and we prove global existence and stability results for solutions of this system. In the particular case of the Euler-Poisson system in the attractive regime our approach yields an explicit representation formula for the solutions. 
Yann Brenier, Wilfrid Gangbo, Giuseppe Savar\'e, Michael   Westdickenberg
math.AP math-ph math.MP