Abstract
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 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 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 a priori energy bounds.