Calculus of Variations and Geometric Measure Theory

Y. Brenier - W. Gangbo - G. Savaré - M. Westdickenberg

Sticky particle dynamics with interactions

created by savare on 24 Feb 2021



Inserted: 24 feb 2021

Year: 2012

ArXiv: 1201.2350 PDF


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.