Calculus of Variations and Geometric Measure Theory
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Y. Brenier - W. Gangbo - G. Savaré - M. Westdickenberg

Sticky particle dynamics with interactions

created by savare on 24 Feb 2021

[BibTeX]

preprint

Inserted: 24 feb 2021

Year: 2012

ArXiv: 1201.2350 PDF

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.

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