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We prove nonlinear stability of compactly supported expanding star-solutionsof the mass-critical gravitational Euler-Poisson system. These specialsolutions were discovered by Goldreich and Weber in 1980. The expanding rate ofsuch solutions can be either self-similar or non-self-similar (linear), and wetreat both types. An important outcome of our stability results is theexistence of a new class of global-in-time radially symmetric solutions, whichare not homogeneous and therefore not encompassed by the existing works. UsingLagrangian coordinates we reformulate the associated free-boundary problem as adegenerate quasilinear wave equation on a compact spatial domain. The problemis mass-critical with respect to an invariant rescaling and the analysis iscarried out in similarity variables.

Nonlinear stability of expanding star solutions in the radially-symmetric mass-critical Euler-Poisson system