论文标题
近似BGK方程的随机粒子系统
A stochastic particle system approximating the BGK equation
论文作者
论文摘要
我们考虑一个随机的$ n $粒子系统，在圆环上，每个粒子可以自由移动，可以根据该瞬间的粒子构型即时进行热效化。在[2]之后，我们表明混乱的传播确实存在，并且一颗粒子的分布会收敛到BGK方程的溶液。相对于[2]的改进在于以下事实：如物理考虑所暗示的那样，热跃迁仅由跳跃粒子的小邻居中粒子构型的限制驱动。换句话说，传出粒子的麦克斯韦分布是通过与颗粒的分数相关的经验流体动力学场计算得出的，而不是通过整个粒子构型，而不是[2]，而不是[2]中。 [2]：ARXIV：2002.10535（期刊参考：Arch。Cation。Mech。Anal。Vol。240（2021），第785-808页）
We consider a stochastic $N$-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we show that the propagation of chaos does hold and that the one-particle distribution converges to the solution of the BGK equation. The improvement with respect to [2] consists in the fact that here, as suggested by physical considerations, the thermalizing transition is driven only by the restriction of the particle configuration in a small neighborhood of the jumping particle. In other words, the Maxwellian distribution of the outgoing particle is computed via the empirical hydrodynamical fields associated to the fraction of particles sufficiently close to the test particle and not, as in [2], via the whole particle configuration. [2]: arXiv:2002.10535 (Journal reference: Arch. Ration. Mech. Anal. Vol. 240 (2021), pp. 785-808)
