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Existence of positive solutions and hydrodynamic limit of the steady Boltzmann equation with in-flow boundary condition
  • Chenghong Wang,
  • Fujun ZHOU,
  • Weijun Wu
Chenghong Wang
South China University of Technology
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Fujun ZHOU
South China University of Technology
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Weijun Wu
South China University of Technology
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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.