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Existence of global solutions for the space inhomogeneous Enskog equation. (English) Zbl 0629.76083

As is well known, global existence theorems are lacking for the nonlinear Boltzmann equation in the space inhomogeneous case, unless the initial data are a perturbation of an equilibrium state or a vacuum. To these cases one can add the solutions corresponding to very special initial data for which a priori bounds on the density can be established. Further solutions have been obtained by nonstandard analysis but then it is not clear whether the solutions can develop singularities in a finite time. The entire field of kinetic is the subject of intense study and new important results can be expected each week. The paper under consideration was presented at a meeting held in Paris in 1985 and published with a considerable delay. It presents an existence theorem for global solutions of the Enskog equation (proposed by Enskog in 1921 to replace the Boltzmann equation for hard spheres in the case of a dense gas). The solutions are assumed to depend on just one space variable and to possess finite mass, density and entropy. The data are otherwise arbitrary.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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