Mathematics – Analysis of PDEs
Scientific paper
2012-01-11
Mathematics
Analysis of PDEs
Scientific paper
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.
Brenier Yann
Gangbo Wilfrid
Savar'e Giuseppe
Westdickenberg Michael
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