标题： 具有准共振碰撞的多原子气体的动能模型导致双温度松弛过程 显示英文标题

标题： A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes

摘要： 本文中，我们通过引入准共振核来扩展多原子气体的玻尔兹曼框架，这些准共振核放松了共振相互作用，在这些相互作用中动能和内能分别守恒，并导致具有两个温度的平衡态。 我们建立了H定理，并分析了准共振模型的渐近行为，展示了两阶段松弛过程：初始收敛到双温度麦克斯韦分布状态，随后两个温度逐渐向彼此松弛。 数值模拟验证了我们的理论预测。 准共振的概念提供了玻尔兹曼动力学的第一个严格框架，其中分布始终接近一个多温度麦克斯韦分布，并向单温度麦克斯韦分布松弛。 显示英文摘要

摘要： In this article, we extend the Boltzmann framework for polyatomic gases by introducing quasi-resonant kernels, which relax resonant interactions, for which kinetic and internal energies are separately conserved and lead to equilibrium states with two temperatures. We establish an H-theorem and analyze the quasi-resonant model's asymptotic behaviour, demonstrating a two-phase relaxation process: an initial convergence towards a two-temperature Maxwellian state followed by gradual relaxation of the two temperatures towards each other. Numerical simulations validate our theoretical predictions. The notion of quasi-resonance provides the first rigorous framework of a Boltzmann dynamics for which the distribution is at all times close to a multi-temperature Maxwellian, relaxing towards a one-temperature Maxwellian.