  We here investigate a modification of the compressible barotropic Euler
system with friction, involving a fuzzy nonlocal pressure term in place of the
conventional one. This nonlocal term is parameterized by $\epsilon$ > 0 and
formally tends to the classical pressure when $\epsilon$ approaches zero. The
central challenge is to establish that this system is a reliable approximation
of the classical compressible Euler system. We establish the global existence
and uniqueness of regular solutions in the neighborhood of the static state
with density 1 and null velocity. Our results are demonstrated independently of
the parameter $\epsilon$, which enable us to prove the convergence of solutions
to those of the classical Euler system. Another consequence is the rigorous
justification of the convergence of the mass equation to various versions of
the porous media equation in the asymptotic limit where the friction tends to
infinity. Note that our results are demonstrated in the whole space, which
necessitates the use of a suitable L^1-in-time space framework.
