The two-dimensional Euler-Poisson system with spherical symmetry.

This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay (1 + t)-1 of the linear system. Inspired by the work of Ozawa et al., ['Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions,' Math. Z. 222, 341-362 (1996); 'Remarks on the Klein-Gordon equation with quadratic nonlinearity in two space dimensions,' in Nonlinear Waves, Gakuto International Series: Mathematical Sciences and Applications Vol. 10 (Gakkotosho, Tokyo, 1997), pp. 383-392,] we show that such smooth solutions exist for radially symmetric flows. [ABSTRACT FROM AUTHOR]

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