## Y. Brenier - W. Gangbo - G. SavarÃ© - M. Westdickenberg

# Sticky particle dynamics with interactions

created by savare on 24 Feb 2021

[

BibTeX]

*preprint*

**Inserted:** 24 feb 2021

**Year:** 2012

**Abstract:**

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.