Stability of Global Solution for the Relativistic Enskog Equation near Vacuum

The Cauchy problem of the relativistic Enskog equation with near-vacuum data is considered in this paper. Under the same assumption as that in Jiang (J. Stat. Phys. 127: 805-812, 2007) for the relativistic Enskog equation, we obtain the uniform L-infinity-stability of the solution. What's more important, is that for two new types of the scattering cross section sigma, we give the global existence and L-1(x, v)-stability for mild solution when the initial data lies in the space L-1(x, v). As a corollary, we have a BV-type estimate. It is worth mentioning that the stability results in this paper can be applied to the case in Jiang (J. Stat. Phys. 127: 805-812, 2007).