for smooth data close to equilibrium and by Hoff in the case of discontinuous data in [@5H2; @5H3]. All those results do not require to be far from the vacuum. The existence and uniqueness of local classical solutions for (\[0.1\]) with smooth initial data such that the density $\rho_{0}$ is bounded and bounded away from zero (i.e., $0<\underline{\rho}\leq\rho_{0}\leq M$) has been stated by Nash in [@Nash]. Let us emphasize that no stability condition was required there. On the other hand, for small smooth perturbations of a stable equilibrium with constant positive density, global well-posedness has been proved in [@MN]. Many works on the case of the one dimension have been devoted to the qualitative behavior of solutions for large time (see for example [@5H1; @5K]). Refined functional analysis has been used for the last decades, ranging from Sobolev, Besov, Lorentz and Triebel spaces to describe the regularity and long time behavior of solutions to the compressible model [@5So], [@5V], [@5H4], [@5K1]. Let us recall that (local) existence and uniqueness for (\[0.1\]) in the case of smooth data with no vacuum has been stated for long in the pioneering works by J. Nash [@Nash], and A. Matsumura, T. Nishida [@MN].\
Guided 