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We are concerned with a global existence theory for finite-energy solutionsof the multidimensional Euler-Poisson equations for both compressible gaseousstars and plasmas with large initial data of spherical symmetry. One of themain challenges is the strengthening of waves as they move radially inwardtowards the origin, especially under the self-consistent gravitational fieldfor gaseous stars. A fundamental unsolved problem is whether the density of theglobal solution forms a delta measure ({\it i.e.}, concentration) at theorigin. To solve this problem, we develop a new approach for the constructionof approximate solutions as the solutions of an appropriately formulated freeboundary problem for the compressible Navier-Stokes-Poisson equations with acarefully adapted class of degenerate density-dependent viscosity terms, sothat a rigorous convergence proof of the approximate solutions to thecorresponding global solution of the compressible Euler-Poisson equations withlarge initial data of spherical symmetry can be obtained. Even though thedensity may blow up near the origin at a certain time, it is proved that nodelta measure ({\it i.e.}, concentration) in space-time is formed in thevanishing viscosity limit for the finite-energy solutions of the compressibleEuler-Poisson equations for both gaseous stars and plasmas in the physicalregimes under consideration.

Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry