  In this paper, we prove the global existence of analytical solutions to the
compressible Oldroyd-B model without retardation near a non-vacuum equilibrium
in ${\mathbb R}^n$ $(n=2,3)$. Zero retardation results in zero dissipation in
the velocity equation, which is the main difficulty that prevents us to obtain
the long time well-posedness of solutions. Through dedicated analysis, we find
that the linearized equations of this model have damping effects, which ensures
the global-in-time existence of small data solutions. However, the nonlinear
quadratic terms have one more order derivative than the linear part and no good
structure is discovered to overcome this derivative loss problem. So we can
only build the result in the analytical energy space rather than Sobolev space
with finite order derivatives.
