Sticky particle dynamics with interactions

Details Sticky particle dynamics with interactions Sticky particle dynamics with interactions

2012-01-11

arxiv.org/abs/1201.2350v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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