标题： 玻尔兹曼边界层方程与麦克斯韦反射边界条件及在流体极限中的应用 显示英文标题

标题： Boltzmann boundary layer equation with Maxwell reflection boundary condition and applications to fluid limits

摘要： 本文研究了半空间中的Knudsen层方程，该方程来源于Boltzmann方程到流体动力学的流体极限。 我们考虑具有accommodation系数$0<\alpha<1$的Maxwell反射边界条件。 我们专注于具有角截断的硬球碰撞，证明了在$L^{\infty}_{x,v}$中解的存在性、唯一性和渐近行为。 此外，我们通过一个具体例子展示了定理在流体极限中的应用。 在这个例子中，我们利用我们的定理和Knudsen层方程对于$\alpha\in(0,1]$和$\alpha=O(1)$的对称性质推导出流体方程的边界条件。 这些推导与镜面反射和几乎镜面反射的情况有显著不同。 这明确地描述了在\cite{jiang2024knudsenboundarylayerequations}中定义的{\em 衰减源集} 显示英文摘要

摘要： This paper investigates the Knudsen layer equation in half-space, arising from the hydrodynamic limit of the Boltzmann equation to fluid dynamics. We consider the Maxwell reflection boundary condition with accommodation coefficient $0<\alpha<1$. We restrict our attention to hard sphere collisions with angular cutoff, proving the existence, uniqueness, and asymptotic behavior of the solution in $L^{\infty}_{x,v}$. Additionally, we demonstrate the application of our theorem to the hydrodynamic limit through a specific example. In this expample, we derive the boundary conditions of the fluid equations using our theorem and the symmetric properties of the Knudsen layer equation for $\alpha\in(0,1]$ and $\alpha=O(1)$. These derivations differs significantly from the cases of specular and almost specular reflection. This explicitly characterizes the {\em vanishing sources set} defined in \cite{jiang2024knudsenboundarylayerequations}