从非马尔可夫系统到朗道方程
From a non-Markovian system to the Landau equation
摘要：
本文证明了在一阶宏观时间内，截断BBGKY族（到二阶）的解在弱耦合极限内收敛到非线性空间齐次Landau方程的解.截断问题描述了底层粒子动力学的形式领先阶行为，可以重新表述为一个非马尔可夫双曲方程，它收敛到抛物朗道方程描述的马尔可夫演化。在本文中的分析是出于Bogolyubov的动力学方程的推导通过BBGKY层次的多时间尺度分析。
英文摘要：
In this paper, we prove that in macroscopic times of order one, the solutions to the truncated BBGKY hierarchy (to second order) converge in the weak coupling limit to the solution of the nonlinear spatially homogeneous Landau equation. The truncated problem describes the formal leading order behavior of the underlying particle dynamics and can be reformulated as a non-Markovian hyperbolic equation, which converges to the Markovian evolution described by the parabolic Landau equation. The analysis in this paper is motivated by Bogolyubov's derivation of the kinetic equation by means of a multiple time scale analysis of the BBGKY hierarchy.
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