Compressible flow and Euler's equations

Abstract

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the inverse density of the wave fronts vanishes and the shocks form. We obtain a detailed description of the geometry of this singular boundary and a detailed analysis of the behavior of the solution there.