In this paper we prove the convergence of a suitable particle system towards the BGK model. More precisely, we consider an interacting stochastic particle system in which each particle can instantaneously thermalize locally. We show that, under a suitable scaling limit, propagation of chaos does hold and the one-particle distribution function converges to the solution of the BGK equation.

中文翻译：

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BGK方程的粒子逼近

在本文中，我们证明了合适的粒子系统对BGK模型的收敛性。更准确地说，我们考虑一个相互作用的随机粒子系统，其中每个粒子都可以瞬间局部热化。我们表明，在适当的缩放限制下，混沌的传播确实成立，并且单粒子分布函数收敛到BGK方程的解。