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Global solutions of the Boltzmann equation in a bounded convex domain. (English) Zbl 0382.35047

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35Q30 Navier-Stokes equations
35B99 Qualitative properties of solutions to partial differential equations
82B40 Kinetic theory of gases in equilibrium statistical mechanics
82B05 Classical equilibrium statistical mechanics (general)
76S05 Flows in porous media; filtration; seepage
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[1] H. Grad: Asymptotic theory of the Boltzmann equation. II. Rarefied Gas Dynamics, 1 (J. A. Laurmann, Ed.), Academic Press, New York (1963). · Zbl 0115.45006 · doi:10.1063/1.1706716
[2] H. Grad: Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equation. Proceedings of Symposia in Applied Mathematics, 17, Amer. Math. Soc, Providence (1965). · Zbl 0144.48203
[3] J. P. Guiraud: An H theorem for a gas of rigid spheres in a bounded domain. Theories Cinetiques Classiques et Relativistes, C. N. R. S., Paris (1975). · Zbl 0364.76067
[4] Y. Shizuta: On the classical solutions of the Boltzmann equation (to appear in Comm. Pure Appl. Math.). · Zbl 0515.35002 · doi:10.1002/cpa.3160360602
[5] Y. Shizuta: The existence and approach to equilibrium of classical solutions of the Boltzmann equation (to appear in Comm. Math. Phys.).
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