  We study the resolution of discontinuous singularities in gas dynamics via
rarefaction waves. The mechanism is well-understood in the one dimensional
case. We will prove the non-nonlinear stability of the Riemann problem for
multi-dimensional isentropic Euler equations in the regime of rarefaction
waves. The proof relies on the new energy estimates \emph{without loss of
derivatives}. We also give a detailed geometric description of the rarefaction
wave fronts. This is the first paper in the series which provides the \emph{a
priori} energy bounds.
