  The general problem of shock formation in three space dimensions was solved
by D. Christodoulou in his 2007 monograph: 'The Formation of Shocks in
3-dimensional Fluids'. In this work also a complete description of the maximal
development of the initial data is provided. This description sets up the
problem of continuing the solution beyond the point where the solution ceases
to be regular. This problem is called the shock development problem. It belongs
to the category of free boundary problems but possesses the additional property
of having singular initial data due to the behavior of the solution at the
blowup surface. The present work delivers the solution to this problem in the
case of spherical symmetry for a barotropic fluid. A complete description of
the singularities associated to the development of shocks in terms of smooth
functions is given.
