Abstract. By extension of the three-dimensional analytical solutions of Goldreich and Weber (1980 Homologously collapsing stellar cores Astrophys. J. 238 991) with an adiabatic exponent γ = 4/3, to the (classical) Euler–Poisson equations without a cosmological constant, the self-similar (almost re-collapsing) time-periodic solutions with a negative cosmological constant (Λ < 0) are constructed. The solutions with time periodicity are novel. Based on these solutions, the time-periodic and almost re-collapsing model is conjectured in this paper, for some gaseous stars.

PACS numbers: 98.10.+z, 98.80.Jk, 02.30.Jr, 02.30.Hq

Mathematics Subject Classification: 85A15, 35C05, 35B40, 35Q30, 76D05

Print publication: Issue 23 (7 December 2009)
Received 11 June 2009, in final form 31 July 2009
Published 6 November 2009