论文标题
相对论鲍尔茨曼方程的全局良好性，具有分散反射边界条件在有限域中
The Global Well-Posedness of the Relativistic Boltzmann Equation with Diffuse Reflection Boundary Condition in Bounded Domains
论文作者
论文摘要
有限域中的相对论玻尔兹曼方程已被广泛用于物理和工程中，例如，融合反应器中的Tokamak设备。尽管它的重要性，但据我们所知，没有关于求解对相对性Boltzmann方程的全球求解的数学理论。在本文中，假设一个有界域中的相对论颗粒的运动受相对论鲍尔茨曼方程的支配，该方程具有较小变化的非等温壁温度的弥漫反射边界条件，围绕正常的常数，以及光的速度，y mathfrak {c} $，我们首先构建了一个独特的速度，我们是独一无二的。 $ f _ {*} $，并进一步建立具有指数时间衰减率的这种固定解决方案的动态稳定性。我们指出，$ l^{\ infty} $ - 稳定和非稳态解决方案的扰动限制与光$ \ mathfrak {C} $的速度无关，并且在$ \ mathfrak {C} $估计中，这种均匀的估计值将在未来对牛顿限制的研究中有用。
The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors.In spite of its importance, there has, to the best of our knowledge, been no mathematical theory on the global existence of solutions to the relativistic Boltzmann equation in bounded domains. In the present paper, assuming that the motion of single-species relativistic particles in a bounded domain is governed by the relativistic Boltzmann equation with diffuse reflection boundary conditions of non-isothermal wall temperature of small variations around a positive constant, and regarding the speed of light $\mathfrak{c}$ as a large parameter, we first construct a unique non-negative stationary solution $F_{*}$, and further establish the dynamical stability of such stationary solution with exponential time decay rate. We point out that the $L^{\infty}$-bound of perturbations for both steady and non-steady solutions are independent of the speed of light $\mathfrak{c}$, and such uniform in $\mathfrak{c}$ estimates will be useful in the study of Newtonian limit in the future.
