Global existence in \(L^ 1\) for the generalized Enskog equation. (English) Zbl 1083.82531

Summary: Various existence theorems are given for the generalized Enskog equation in \(\mathbb{R}^3\) and in a bounded spatial domain with periodic boundary conditions. A very general form of the geometric factor \(Y\) is allowed, including an explicit space, velocity, and time dependence. The method is based on the existence of a Lyapunov functional, an analog of the \(H\) function in the Boltzmann equation, and utilizes a weak compactness argument in \(L^1\).


82C40 Kinetic theory of gases in time-dependent statistical mechanics
35Q99 Partial differential equations of mathematical physics and other areas of application
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