Pointwise estimates of solutions for the Euler-Poisson equations with damping in multi-dimensions

Abstract

The global existence and pointwise estimates of the Cauchy problem for the Euler-Poisson equation with damping in multi-dimensions are considered. Based on the analysis of Green function, and using the special structure of the system together with weighted energy method, we obtain the global existence of the classical solution. What's more important, is that we derive a detailed, pointwise description of asymptotic behavior of the solutions of the Cauchy problem. Then we obtain the optimal $L^p(R^n)\ (p>\frac{n}{n-1})$ convergence rate of the solutions.