Boundary effects play an important role in the study of hydrodynamic limits in the Boltzmann theory. Based on a systematic study of the viscous layer equations and the \(L^2\) to \(L^\infty \) framework, we establish the validity of the Hilbert expansion for the Boltzmann equation with specular reflection boundary conditions, which leads to derivations of compressible Euler equations and acoustic equations in half-space.

中文翻译：

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半空间中具有镜面边界条件的Boltzmann方程的Hilbert展开

边界效应在玻耳兹曼理论中对水动力极限的研究中起着重要作用。在对粘性层方程和\（L ^ 2 \）到\（L ^ \ infty \）框架进行系统研究的基础上，我们建立了具有镜面反射边界条件的Boltzmann方程的希尔伯特展开的有效性，这导致了半空间中可压缩的欧拉方程和声学方程的推导。