Global solutions near Maxwellians are constructed for the Boltzmann equation in an infinite layer with diffuse reflection boundaries, with heat-equation-type decay in the 3D case and existence without decay in the 2D case.
Cercignani, On the initial-boundary value problem for the Boltzmann equation , Archive for Rational Mechanics and Analysis, 116 (1992), pp
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Global dynamics of isothermal rarefied gas flows in an infinite layer
Global solutions near Maxwellians are constructed for the Boltzmann equation in an infinite layer with diffuse reflection boundaries, with heat-equation-type decay in the 3D case and existence without decay in the 2D case.