Global existence inL 1 for the modified nonlinear Enskog equation in ?3

Abstract

A global existence theorem with large initial data inL1 is given for the modified Enskog equation in ℝ3. The method, which is based on the existence of a Liapunov functional (analog of theH-Boltzmann theorem), utilizes a weak compactness argument inL1 in a similar way to the DiPerna-Lions proof for the Boltzmann equation. The existence theorem is obtained under certain condition on the behavior of the geometric factorY. The condition onY amounts to the fact that theL1 norm of the collision term grows linearly when the local density tends to infinity.