assumption that starless cores can be in a collapsing prestellar or in an unbounded stage while protostellar cores contain relatively hot hydrostatic gas-dust spheresthe precursors of T-Tauri stars-and outflows (Belloche et al., 2011a, b). After a time between 10 5 and 10 6 years the gaseous envelope disappears and a T-Tauri star surrounded by a turbulent disk becomes observable. Our SN-model is based on these three stages of lowmass star formation (Fig. 1). Its early part simulates the starless stage as a quasi-stationary cloud core and the protostellar stage as a collapsing cloud core. The material in each stage consists of the gas phase with about 99% of the total core mass and the dust phase. Both phases interact with each other thermally and chemically. The energetic equilibrium of the first stage corresponds to a spherical core constructed by Bonnor (1956) and Ebert (1957). Since a number of these cores are characterized by oscillations (Keto et al., 2006), which are mathematically similar to stellar pulsations, relatively long lifetimes