Mathematical Theory Of Relativistic Euler-Poisson Equations

The introduction is given in Chapter one.In chapter2, we consider the existence and uniqueness of smooth steady state so-lution, and their non-relativistic limit, zero-relaxation limit as well as convergence ratesof each limit.In chapter3, we study the existence and the asymptotic behavior of global smoothsolution to the initial boundary value problem of the relativistic Euler-Poisson equations.We obtain that the global smooth solution exists and converges to the smooth steady statesolution in time exponentially fast as t�'∞.In chapter4, we consider asymptotic limits of the relativistic Euler-Poisson equa-tions. We obtain the results on the non-relativistic limit, which is that the global smoothsolution of the relativistic Euler-Poisson equations converges to the subsonic globalsmooth solution of the classical Euler-Poisson equations, as well as the combined zero-relaxation and non-relativistic limit of global smooth solutions to the relativistic Euler-Poisson equations when the initial data is the small perturbation of the given steady statesolution and the boundary strength δ=|φr|+|ρr ρl|is suitably small.