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Spacetime without reference frames: An application to the kinetic theory. (English) Zbl 0878.70014

Summary: Spacetime structures defined in the language of manifolds admit an absolute formulation, i.e., a formulation which does not refer to observer (reference frames). We consider an affine structure for Galilean spacetime. As an application, the Chapman-Enskog iteration for the solution of the Boltzmann equation is given in an absolute form. As a consequence, the second approximations of the stress tensor and the heat flux are obtained in a form independent of observers, which throws new light on material frame indifference.

MSC:

70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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