From Particle Systems to the Landau Equation: A Consistency Result

被引：0
作者：
A. V. Boblylev
M. Pulvirenti
C. Saffirio
机构：
[1] Karlstad University,Department of Mathematics
[2] Università di Roma “La Sapienza”,Dipartimento di Matematica
来源：
Communications in Mathematical Physics | 2013年 / 319卷
关键词：
Boltzmann Equation; Particle System; Landau Equation; Homogeneous Boltzmann Equation; Hard Potential;
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摘要：
We consider a system of N classical particles, interacting via a smooth, short-range potential, in a weak-coupling regime. This means that N tends to infinity when the interaction is suitably rescaled. The j-particle marginals, which obey the usual BBGKY hierarchy, are decomposed into two contributions: one small but strongly oscillating, the other hopefully smooth. Eliminating the first, we arrive to establish the dynamical problem in terms of a new hierarchy (for the smooth part) involving a memory term. We show that the first order correction to the free flow converges, as N →∞, to the corresponding term associated to the Landau equation. We also show the related propagation of chaos.
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页码：683 / 702
页数：19
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共 35 条
  • [1] Arsen’ev A.A.(1990)On a connection between the solution of the Boltzmann equation and the solution of the Landau–Fokker–Planck equation (in Russian) Mat. Sb 181 435-446
  • [2] Buryak O.E.(2004)Some considerations on the derivation of the nonlinear quantum Boltzmann equation J. Stat. Phys. 116 381-410
  • [3] Benedetto D.(2005)On the weak-coupling limit for bosons and fermions Math. Mod. Meth. Appl. Sci. 15 1-33
  • [4] Castella F.(2008)From the N-body Schrödinger equation to the quantum Boltzmann equation: a term-by-term convergence result in the weak coupling regime Commun. Math. Phys. 277 1-44
  • [5] Esposito R.(1992)The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case Math. Mod. Meth. Appl. Sci. 2 167-182
  • [6] Pulvirenti M.(2000)On the spatially homogeneous Landau equation for hard potentials. II. Comm. Part. Diff. Eqs. 25 261-298
  • [7] Benedetto D.(2000)-theorem and applications Comm. Part. Diff. Eqs. 25 179-259
  • [8] Castella F.(1987)On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness Commun. Math. Phys. 113 209-230
  • [9] Esposito R.(2004)Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model J. Stat. Phys. 116 367-380
  • [10] Pulvirenti M.(1997)On the quantum Boltzmann equation J. Stat. Phys. 89 751-776
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