Demetrios Christodoulou

Abstract:   In this talk I shall present, in summary form, my recent monograph, which considers the relativistic Euler equations for the motion of a perfect fluid with an arbitrary equation of state. The initial data, given on a spacelike hyperplane in 4-dimensional Minkowski spacetime, are assumed to coincide with the data corresponding to a constant state outside a sphere. Under a suitable restriction on the size of the departure of the initial data from those of the constant state, certain theorems are established, which describe the maximal classical development of the initial data. In particular the theorems describe the geometry of the boundary of the domain of the maximal classical development and analyze the behavior of the solution at this boundary. A complete picture of shock formation in 3-dimensional fluids is in this way obtained.