On the Enskog Equation with Large Initial Data

This paper is concerned with the Enskog equation with large initial data in $L^1 $, where the high density factor is constant. As a preliminary step, existence and uniqueness is first studied in full physical space and in a box with periodic boundary conditions under the restriction of bounded velocities, by the use of a priori estimates in the norm $\int {(\sup _{0 \leqq t \leqq T} {f(x + tv,v,t)} |)dx\,dv} $. Global existence and uniqueness for small data and unbounded velocities is an easy consequence of this step. The rest of the paper is devoted to the central topic: global existence, regularity, and uniqueness for large initial data in full physical space for the case of unbounded velocities, provided all v-moments are initially finite. Here the more detailed structure of the collision operator is exploited in the a priori estimates.