论文标题
部分可观测时空混沌系统的无模型预测
Global bounded solutions to the Boltzmann equation for a polyatomic gas
论文作者
论文摘要
在本文中，我们考虑了对多原子气体的运动进行建模的Boltzmann方程，其中集成碰撞操作员与经典的碰撞操作员相比涉及一个额外的内部能量变量$ i \ in \ Mathbb {r} _+$和一个参数$δ\ geq 2 $。在扰动框架中，我们建立了在全球均衡环境附近的全球适应性解决方案。证明基于$ l^2 \ cap l^\ infty $方法。确切地说，我们首先研究了线性方程式的$ l^2 $衰减属性，然后使用线性整体操作员的迭代技术来获得线性加权$ l^\ infty $ decay，并最终获得$ l^\ infty $绑定的限制，以及解决方案的非线性时间衰减，以使其与duemiple of duamel of Duhamel sarf fors fors the fors the Dureamel sarf fors fors fors the fors fors the fors fors thr pross fors fors the pross thr thr pross thr thr pross fors thr pross fors thr trist。在整个证明过程中，我们进行了仔细的分析，用于处理内部能量变量$ i $和参数$δ$的额外效果。
In this paper we consider the Boltzmann equation modelling the motion of a polyatomic gas where the integration collision operator in comparison with the classical one involves an additional internal energy variable $I\in\mathbb{R}_+$ and a parameter $δ\geq 2$ standing for the degree of freedom. In perturbation framework, we establish the global well-posedness for bounded mild solutions near global equilibria on torus. The proof is based on the $L^2\cap L^\infty$ approach. Precisely, we first study the $L^2$ decay property for the linearized equation, then use the iteration technique for the linear integral operator to get the linear weighted $L^\infty$ decay, and in the end obtain $L^\infty$ bounds as well as exponential time decay of solutions for the nonlinear problem with the help of the Duhamel's principle. Throughout the proof, we present a careful analysis for treating the extra effect of internal energy variable $I$ and the parameter $δ$.
