Hydrodynamic limit with geometric correction of stationary Boltzmann equation. (English) Zbl 1336.35272
Summary: We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in \(L^\infty\) both for its proof and result. Also, we show the hydrodynamic limit with a different boundary layer expansion with geometric correction.
MSC:
| 35Q20 | Boltzmann equations |
| 35L65 | Hyperbolic conservation laws |
| 82B40 | Kinetic theory of gases in equilibrium statistical mechanics |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
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