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September  2010, 26(3): 1101-1117. doi: 10.3934/dcds.2010.26.1101

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

Zhigang Wu 1, and  Weike Wang 2,

1. 

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2. 

Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, 200240, Shanghai

Received  January 2009 Revised  August 2009 Published  December 2009

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.
Keywords: Green function, Euler-Poisson equations, multi-dimensions, pointwise estimates..
Mathematics Subject Classification: Primary: 35Q05, 35M11; Secondary: 42B2.
Citation: Zhigang Wu, Weike Wang. Pointwise estimates of solutions for the Euler-Poisson equations with damping in multi-dimensions. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 1101-1117. doi: 10.3934/dcds.2010.26.1101
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