The paper derives beta-dependent slip boundary conditions for compressible Navier-Stokes from the Boltzmann equation with almost specular Maxwell reflection, and rigorously proves the specular-reflection approximation in bounded domains.
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Compressible Navier-Stokes system with slip boundary from Boltzmann equations with reflection boundary: derivations and justifications
The paper derives beta-dependent slip boundary conditions for compressible Navier-Stokes from the Boltzmann equation with almost specular Maxwell reflection, and rigorously proves the specular-reflection approximation in bounded domains.