Spectral observations of molecular line profiles reveal the so-called ‘blue profiles’ for double-peaked molecular spectral lines with stronger blue and weaker red peaks as notable features for star-forming cloud core collapses under the self-gravity. In contrast, ∼25–30 per cent of observed molecular spectral line profiles in star-forming clouds or cores also show the so-called double-peaked ‘red profiles’ with red peaks stronger than blue peaks. Gao & Lou show that these unexplained ‘red profiles’ can be signatures of global self-similar dynamics for envelope expansion with core collapse (EECC) within star-forming molecular clouds or cores. We demonstrate here that spatially resolved ‘red profiles’ of HCO+ (J= 1–0) and CS (J= 2–1) molecular transitions from the low-mass star-forming cloud core FeSt 1−457 together with its radial profile of column density inferred from dust extinction observations appear to reveal a self-similar hydrodynamic shock phase for global EECC. Observed spectral profiles of C18O (J= 1–0) are also fitted by the same EECC model. For further observational tests, the spatially resolved profiles of molecular transitions HCO+ (J= 3–2) and CS (J= 3–2) as well as the radial profiles of (sub)millimetre continuum emissions at three wavelengths of 1.2, 0.85 and 0.45 mm from FeSt 1−457 are also predicted.