论文标题
Boltzmann方程的介质相互作用和散射解决方案的演变
Evolution of mesoscopic interactions and scattering solutions of the Boltzmann equation
论文作者
论文摘要
本文的目的是研究在介质量表上移动相互作用颗粒的演变。我们将引入一个不确定性原理和一个新的先验结合，以使颗粒的演变受到一般介镜相互作用，并使用此设置来证明在没有传统方法（如速度平均速度或strichartz-type估计值）的情况下，颗粒的普遍分散证据。我们将在通用性方面发展一个散射理论，并利用其框架工作来展示boltzmann方程的类散射解决方案的存在和独特性，并在$ l^{\ infty} $设置中具有渐近稳定性和完整性。
The purpose of this paper is to study the evolution of moving interacting particles on the mesoscopic scale. We will introduce an uncertainty principle and a new priori bound for the evolution of particles subject to a general mesoscopic interaction and use this setting to demonstrate evidence for the universal dispersion of particles in the absence of the conventional methods like velocity averaging lemmas or Strichartz-type estimates. We will develop a scattering theory in generality and use its frame work to show the existence and uniqueness of a class scattering solutions to the Boltzmann equation with asymptotic stability and completeness in the $L^{\infty}$ setting.
