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arXiv · 1201.2350

Sticky particle dynamics with interactions

Yann Brenier·Wilfrid Gangbo·Giuseppe Savaré·Michael Westdickenberg
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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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Yann Brenier, Wilfrid Gangbo, Giuseppe Savaré, Michael Westdickenberg. 2012-01-11. Sticky particle dynamics with interactions. https://doi.org/10.1016/j.matpur.2012.09.013

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