Consider the stationary Boltzmann equation in 2-dimensional convex domains with diffusive boundary condition. We establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier–Stokes–Fourier system with nonslip boundary conditions. Our contribution focuses on novel weighted $W^{1,\infty }$ estimates for the $𝜖$-Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an $L^{2m}$-$L^{\infty }$ framework.

中文翻译：

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二维凸域中玻尔兹曼方程的边界层

考虑具有扩散边界条件的二维凸域中的平稳 Boltzmann 方程。我们在边界层存在时建立流体​​动力学极限，并推导出具有防滑边界条件的稳定 Navier-Stokes-Fourier 系统。我们的贡献集中在小说加权${宽}^{1,\infty }$ 估计数 $𝜖$-带有几何校正的米尔恩问题。此外，我们基于${升}^{2米}$——${升}^{\infty }$ 框架。