We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimen- sion. 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.

Sticky particle dynamics with interactions

SAVARE', GIUSEPPE;
2013-01-01

Abstract

We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimen- sion. 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/680262
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