标题： Boltzmann方程在半空间中具有软势能和镜面边界条件的Hilbert展开 显示英文标题

标题： Hilbert Expansion of Boltzmann Equation with Soft Potentials and Specular Boundary Condition in Half-space

摘要： 边界效应在玻尔兹曼理论中流体力学极限的研究中起着重要作用。 我们通过多尺度的希尔伯特展开，严格证明了软势能玻尔兹曼方程到可压缩欧拉方程的流体力学极限的有效性。 具体而言，玻尔兹曼解被分为三部分：内部部分、粘性边界层和克努森边界层。 由于软势能碰撞频率的弱效应，在处理具有空间衰减率的克努森层解的存在性时出现了新的困难，这在一些约束条件和失去速度权重论证下已被克服。 显示英文摘要

摘要： Boundary effects play an important role in the study of hydrodynamic limits in the Boltzmann theory. We justify rigorously the validity of the hydrodynamic limit from the Boltzmann equation of soft potentials to the compressible Euler equations by the Hilbert expansion with multi-scales. Specifically, the Boltzmann solutions are expanded into three parts: interior part, viscous boundary layer and Knudsen boundary layer. Due to the weak effect of collision frequency of soft potentials, new difficulty arises when tackling the existence of Knudsen layer solutions with space decay rate, which has been overcome under some constraint conditions and losing velocity weight arguments.