论文标题
线性化玻尔兹曼碰撞操作员：ii。由连续内部能量建模的多原子分子
Linearized Boltzmann Collision Operator: II. Polyatomic Molecules Modeled by a Continuous Internal Energy Variable
论文作者
论文摘要
单个物种的Boltzmann方程的线性碰撞算子可以写入正乘算子，碰撞频率和紧凑的积分算子的总和。最近，该经典结果扩展到多原子的多原子混合物，其多原子性由离散的内部能量变量建模。在这项工作中，我们证明了多原子单物种的积分算子的紧凑性，多原子性由连续的内部能量变量建模，并且内部自由度的数量更大或等于两个。整体操作员的术语被证明是希尔伯特 - 史密特积分运算符的统一限制。线性化碰撞算子的自相关性随之而来。碰撞频率的固定频率显示出像模型一样的硬球和硬性电势，这意味着线性化碰撞算子的弗雷德霍姆度。
The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently, been extended to multi-component mixtures and polyatomic single species with the polyatomicity modeled by a discrete internal energy variable. In this work we prove compactness of the integral operator for polyatomic single species, with the polyatomicity modeled by a continuous internal energy variable, and the number of internal degrees of freedom greater or equal to two. The terms of the integral operator are shown to be, or be the uniform limit of, Hilbert-Schmidt integral operators. Self-adjointness of the linearized collision operator follows. Coercivity of the collision frequency are shown for hard-sphere like and hard potential with cut-off like models, implying Fredholmness of the linearized collision operator.
