Abstract
We give an outline of the content of our recent monograph “The Shock Development Problem” which analyzes the development of shocks in fluids. The framework is that of Euler’s equations of the mechanics of compressible fluids. We first set up the mathematical problem as an initial-boundary value problem for a nonlinear hyperbolic system of partial differential equations with a free boundary and singular initial conditions. Then we describe the main mathematical methods which we introduce to solve the problem. Some of these methods are geometric and have to do with a geometric structure defined on spacetime by the fluid and its interaction with the background spacetime structure. Also, with the nature of the free boundary and the jump conditions there which include a non-linear jump condition. The central method however is analytic and arises from the need to handle singular integrals appearing in the energy identities.
