Name
Abstract | ||
|---|---|---|
This paper introduces a new method to show the validity of a continuum description for the deterministic dynamics of many interacting particles. Here the many particle evolution is analyzed for a hard sphere ∞ow with the addition that after a col- lision the collided particles are removed from the system. We consider random initial conflgurations which are drawn from a Poisson point process with spatially homogeneous velocity density f0(v). Assuming that the moments of order less than three of f0 are flnite and no mass is concentrated on lines, the homogeneous Boltzmann equation with- out gain term is derived for arbitrary long times in the Boltzmann-Grad scaling. A key element is a characterization of the many particle ∞ow by a hierarchy of trees which en- code the possible collisions. The occurring trees are shown to have favorable properties with a high probability, allowing to restrict the analysis to a flnite number of interacting particles, enabling us to extract a single-body distribution. A counter-example is given for a concentrated initial density f0 even to short-term validity. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s00332-009-9049-y | J. Nonlinear Science |
Keywords | DocType | Volume |
Boltzmann equation,Boltzmann–Grad limit,Validity,Kinetic annihilation,Deterministic dynamics,Random initial data,82C40,76P05,82C22,60K35 | Journal | 20 |
Issue | ISSN | Citations |
1 | 0938-8974 | 1 |
PageRank | References | Authors |
0.63 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Karsten Matthies | 1 | 1 | 2.65 |
| Florian Theil | 2 | 14 | 5.66 |