  Local existence and well posedness for a class of solutions for the Euler
Poisson system is shown. These solutions have a density $\rho$ which either
falls off at infinity or has compact support. The solutions have finite mass,
finite energy functional and include the static spherical solutions for the
adiabatic constant $\gamma=\frac{6}{5}$. The result is achieved by using
weighted Sobolev spaces of fractional order and a new non linear estimate which
allows to estimate the physical density by the regularised non linear matter
variable. Gamblin also has studied this setting but using very different
functional spaces. However we believe that the functional setting we use is
more appropriate to describe a physical isolated body and more suitable to
study the Newtionan limit.
