Existence of positive solutions and hydrodynamic limit of the steady
Boltzmann equation with in-flow boundary condition
Abstract
This work is devoted to the study of existence of positive solutions and
hydrodynamic limit of the steady Boltzmann equation with in-flow
boundary condition. The proof is based on a L6– L∞ framework developed
by [10] and a refined positivity-preserving scheme in deriving
positivity of solutions with in-flow boundary condition and external
force. The incompressible Navier–Stokes–Fourier limit with Dirichlet
boundary condition is justified for in-flow boundary data as small
perturbation of a global Maxwellian.