Passage from the Boltzmann equation with diffuse boundary to the incompressible Euler equation with heat convection
Passage from the Boltzmann equation with diffuse boundary to the incompressible Euler equation with heat convection
复制标题
从具有扩散边界的玻尔兹曼方程到具有热对流的不可压缩欧拉方程
DOI：
10.1016/j.jde.2023.04.028
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发表时间：
2023
影响因子：
2.4
通讯作者：
Kim, Chanwoo
中科院分区：
文献类型：
--
作者：
Cao, Yunbai;Jang, Juhi;Kim, Chanwoo
从流体力学大雷诺数尺度下扩散边界的Boltzmann方程出发，导出了无穿透边界条件下的对流换热不可压缩欧拉方程。受文献[30]中最新框架的启发，我们考虑无滑移边界条件下的Navier-Stokes-Fourier系统作为中间近似，发展了Boltzmann方程在整体Maxwell附近的Hilbert型展开，它允许在极限内通过对流进行非平凡的热传递。为了证明我们的展开式和极限的合理性，采用最近在无粘极限研究中采用的格林函数方法，建立了一个新的直接估计Navier-Stokes-Fourier系统中的热通量及其导数的方法。
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by the recent framework in [30], we consider the Navier-Stokes-Fourier system with no-slip boundary conditions as an intermediary approximation and develop a Hilbert-type expansion of the Boltzmann equation around the global Maxwellian that allows the nontrivial heat transfer by convection in the limit. To justify our expansion and the limit, a new direct estimate of the heat flux and its derivatives in the Navier-Stokes-Fourier system is established adopting a recent Green's function approach in the study of the inviscid limit.