Boundary conditions are investigated for a model gas composed of identical particles with velocities restricted to a given finite set of vectors. A possible model of the gas surface interaction is given and an H theorem for a gas in a vessel is obtained. Then, the steady Couette flow between two parallel plates is studied. The model with four coplanar velocities is used and the velocity set has arbitrary orientation. The exact kinetic solution is compared with the solutions of the associated Navier–Stokes problems.
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Renée Gatignol (1977) studied this question.
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