具有湮灭的Rayleigh气体的动力学描述
Kinetic description of a Rayleigh Gas with annihilation
摘要：
在本文中，我们考虑了一个标记点粒子在气体中的运动硬球，彼此之间没有相互作用的动力学。这个模型被称为理想瑞利气体。我们在这个模型中加入了湮灭的可能性（理想的瑞利气体湮灭），要求每个障碍物要么是湮灭的，要么是弹性的，这决定了标记的粒子是否被弹性反射或从系统中移除。我们提供了一个严格的推导线性玻尔兹曼方程湮没从这个粒子模型中的玻尔兹曼-格拉德极限。此外，我们通过估计阻止Markovianity的配置的贡献，给出了明确的估计在动力学极限的错误。估计表明，该系统可以近似的玻尔兹曼方程的代数长时间尺度上的标度参数。
英文摘要：
In this paper, we consider the dynamics of a tagged point particle in a gas of moving hard-spheres that are non-interacting among each other. This model is known as the ideal Rayleigh gas. We add to this model the possibility of annihilation (ideal Rayleigh gas with annihilation), requiring that each obstacle is either annihilating or elastic, which determines whether the tagged particle is elastically reflected or removed from the system. We provide a rigorous derivation of a linear Boltzmann equation with annihilation from this particle model in the Boltzmann-Grad limit. Moreover, we give explicit estimates for the error in the kinetic limit by estimating the contributions of the configurations which prevent the Markovianity. The estimates show that the system can be approximated by the Boltzmann equation on an algebraically long time scale in the scaling parameter.
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