Global well-posedness of a binary–ternary Boltzmann equation
Global well-posedness of a binary–ternary Boltzmann equation
复制标题
DOI：
10.4171/aihpc/9
复制
发表时间：
2019-10
期刊：
影响因子：
--
通讯作者：
Ioakeim Ampatzoglou;I. Gamba;N. Pavlović;M. Taskovic
中科院分区：
文献类型：
--
作者：
Ioakeim Ampatzoglou;I. Gamba;N. Pavlović;M. Taskovic
本文证明了二元-三元Boltzmann方程在小初值下的整体适定性。二元-三元Boltzmann方程对经典Boltzmann方程进行了修正，同时考虑了二元和三元粒子间的相互作用，可以作为描述非平衡态密度较大气体的更精确的模型。为了证明全局适定性，我们使用Kaniel-Shinbrot迭代和相关工作的解决方案的非线性方程的单调序列的解决方案，适当的线性问题近似。我们表明，三元运营商允许考虑软比二元运营商的潜力，因此我们的解决方案的三元校正的玻尔兹曼方程保留了所有的二元相互作用的解决方案的属性。
In this paper we prove global well-posedness for small initial data for the binary-ternary Boltzmann equation. The binary-ternary Boltzmann equation provides a correction term to the classical Boltzmann equation, taking into account both binary and ternary interactions of particles, and could possibly serve as a more accurate description model for denser gases in non-equilibrium. To prove global well-posedness we use a Kaniel-Shinbrot iteration and related work to approximate the solution of the nonlinear equation by monotone sequences of solutions to appropriate linear problems. We show that the ternary operator allows consideration of softer potentials than the binary operator, consequently our solution to the ternary correction of the Boltzmann equation preserves all the properties of the binary interactions solution.