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arXiv · 2104.02169

Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection

Yunbai Cao·Juhi Jang·Chanwoo Kim
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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.

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Yunbai Cao, Juhi Jang, Chanwoo Kim. 2021-04-05. Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection. https://arxiv.org/abs/2104.02169

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