| 总结: | We are concerned with a global existence theory for finite-energy solutions of the
multidimensional Euler-Poisson equations for both compressible gaseous stars
and plasmas with large initial data of spherical symmetry. One of the main challenges is the strengthening of waves as they move radially inward towards the
origin, especially under the self-consistent gravitational field for gaseous stars.
A fundamental unsolved problem is whether the density of the global solution
forms a delta measure (i.e., concentration) at the origin. To solve this problem, we develop a new approach for the construction of approximate solutions
as the solutions of an appropriately formulated free boundary problem for the
compressible Navier-Stokes-Poisson equations with a carefully adapted class of
degenerate density-dependent viscosity terms, so that a rigorous convergence
proof of the approximate solutions to the corresponding global solution of the
compressible Euler-Poisson equations with large initial data of spherical symmetry can be obtained. Even though the density may blow up near the origin at a
certain time, it is proved that no delta measure (i.e., concentration) in space-time
is formed in the vanishing viscosity limit for the finite-energy solutions of the
compressible Euler-Poisson equations for both gaseous stars and plasmas in the
physical regimes under consideration.
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