Name
Abstract | ||
|---|---|---|
This paper develops a method to rigorously show the validity of continuum description for the deterministic dynamics of many interacting particles with random initial data. We consider a hard sphere flow where particles are removed after the first collision. A fixed number of particles is drawn randomly according to an initial density f(0)( u, v) depending on d-dimensional position u and velocity v. In the Boltzmann-Grad scaling, we derive the validity of a Boltzmann equation without gain term for arbitrary long times, when we assume finiteness of moments up to order two and initial data that are L-infinity in space. We characterize the many-particle flow by collision trees which encode possible collisions. The convergence of the many-particle dynamics to the Boltzmann dynamics is achieved via the convergence of associated probability measures on collision trees. These probability measures satisfy nonlinear Kolmogorov equations, which are shown to be well-posed by semigroup methods. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1137/120865598 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
Boltzmann equation,Boltzmann-Grad limit,validity,kinetic annihilation,deterministic dynamics,random initial data,semigroups,Kolmogorov equation | Boltzmann equation,Nonlinear system,Mathematical analysis,Probability measure,Lattice Boltzmann methods,Collision,Kolmogorov equations,Semigroup,Boltzmann constant,Mathematics | Journal |
Volume | Issue | ISSN |
44 | 6 | 0036-1410 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Karsten Matthies | 1 | 1 | 2.65 |
| Florian Theil | 2 | 14 | 5.66 |