Incompressible Navier–Stokes–Fourier Limit of the Steady Boltzmann Equation with Linear Boundary Condition in an Exterior Domain

Abstract

This paper aims at justifying the incompressible Navier–Stokes–Fourier limit of the steady Boltzmann equation with linear boundary condition in an exterior domain. This generalizes the work Esposito, R., Guo, Y., Marra, R.: Hydrodynamic limit of a kinetic gas flow past an obstacle. Comm. Math. Phys. 364, 765–823 (2018), to the non-isentropic case, in addition with a small external force and a small temperature variation between the wall and infinity. Some new estimates and a refined positivity-preserving scheme are established to construct a unique positive solution to the steady Boltzmann equation. An error estimate is also provided for the small Knudsen number.