论文标题
关于鲍尔茨曼方程的凯奇问题，对多原子气体建模
On the Cauchy problem for Boltzmann equation modelling a polyatomic gas
论文作者
论文摘要
在当前的手稿中，我们考虑了通过引入一个附加连续变量（称为显微镜内部能量）来建模多原子气体的玻尔兹曼方程。我们在整个非线性情况下在空间均匀环境中建立存在和唯一理论，在扩展的毕业生假设对过渡概率率的扩展假设下，这构成了相对速度和内部能量的硬性潜力，并在间隔$（0,2] $中构成速度（0,2] $），这是乘以整合的角度和集成分区的功能。有限的正气体质量和能量，有限的动量以及有限的$ k _*$多项式时刻，$ k _*$，具体取决于过渡概率和多原子分子的结构，多原子分子的结构或其内部自由度，我们在多态度和指出的范围内既有范围又相关。
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogeneous setting for the full non-linear case, under an extended Grad assumption on transition probability rate, that comprises hard potentials for both the relative speed and internal energy with the rate in the interval $(0,2]$, which is multiplied by an integrable angular part and integrable partition functions. The Cauchy problem is resolved by means of an abstract ODE theory in Banach spaces, for an initial data with finite and strictly positive gas mass and energy, finite momentum, and additionally finite $k_*$ polynomial moment, with $k_*$ depending on the rate of the transition probability and the structure of a polyatomic molecule or its internal degrees of freedom. Moreover, we prove that polynomially and exponentially weighted Banach space norms associated to the solution are both generated and propagated uniformly in time.
