Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection
Abstract
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.
Keywords
Cite
@article{arxiv.2104.02169,
title = {Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection},
author = {Yunbai Cao and Juhi Jang and Chanwoo Kim},
journal= {arXiv preprint arXiv:2104.02169},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2005.12192