Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum
- 91 Downloads
We consider a system ofN hard disks in ℝ2 in the Boltzmann-Grad limit (i.e.N → ∞,d ↘ 0,N·d → λ−1>0, whered is the diameter of the disks). If λ is sufficiently small and if the joint distribution densities factorize at time zero, we prove that the time-evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum.
KeywordsNeural Network Statistical Physic Complex System Initial Data Distribution Density
Unable to display preview. Download preview PDF.
- 1.Lanford, O. III: Time evolution of large classical systems. Moser, E. J. (ed.) Lecture Notes in Physics, Vol.38, pp. 1–111. Berlin, Heidelberg, New York: Springer 1975Google Scholar
- 2.Illner, R., Shinbrot, M.: The Boltzmann equation: Global existence for a rare gas in an infinite vacuum. Commun. Math. Phys.95, 217–226 (1984)Google Scholar
- 3.Cercignani, C.: On the Boltzmann equation for Rigid spheres. Transp. Theory Stat. Phys.2, 211–225 (1972)Google Scholar
- 4.Spohn, H.: Boltzmann hierarchy and Boltzmann equation. In: Kinetic theories and the Boltzmann equation. Lecture Notes in Mathematics, Vol.1048, Montecatini 1981 (1984)Google Scholar
- 5.Illner, R., Neunzert, H.: The concept of irreversibility in the kinetic theory of gases, preprint 1985Google Scholar
- 6.Spohn, H.: On the integrated form of the RBGKY hierarchy for hard spheres, unpublishedGoogle Scholar
- 7.Alexander, R. K.: The infinite hard sphere system, Ph.D. Thesis, Department of Mathematics. Berkeley: University of California, 1975Google Scholar
- 8.Marchioro, C., Pellegrinotto, A., Presutti, E., Pulvirenti, M.: On the dynamics of particles in a bounded region: A measure theoretical approach. J. Math. Phys.17, 647–652 (1976)Google Scholar