solutions for initial data with high regularity order and close to a stable equilibrium has been proved by Matsumura and Nishida in [@MN] for three-dimensional polytropic ideal fluids and no outer force. More precisely for $\bar{\rho}>0$, the initial data are choosen small in the following spaces $(\rho_{0}-\bar{\rho},u_{0})\in H^{3}\times H^{3}$. More recently D. Hoff in [@5H4; @5H5] stated the existence of global weak solutions with small initial data including discontinuous initial data (namely $q_{0}$ is small in $L^{2}\cap L^{\infty}$ and $u_{0}$ is small in $L^{4}$ if $N=2$ and small in $L^{8}$ if $N=3$). One of the major interest of the results of Hoff is to get some smoothing effects on the incompressible part of the velocity $u$ and on the effective viscous flux $F=(2\mu+\lambda){\rm div}u-P(\rho)+P(\bar{\rho})$ are also pointed out. D. Hoff is the first author to have introduced the notion of effective flux which play a crucial role in the proof of P-L Lions for the existence of global weak solution. However if the results of Hoff are critical in the sense of the scaling for the density, it is not the case for the initial velocity. In [@5H2], D. Hoff show a very interesting theorem of weak-strong uniqueness when $P(\rho)=K\rho$ 