Characteristic initial value problem for spherically symmetric barotropic flow

We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants, we consider the characteristic form of these equations. In a first part, we show that the resulting constraint equations along characteristics can be solved globally away from the center of symmetry. In a second part, given data on two intersecting characteristics, we show existence and uniqueness of a smooth solution in a neighborhood in the future of these characteristics.