The Shock Development Problem

A fundamental problem in the theory of compressible fluid is to provide a precise description of shock formation and development from smooth initial data. In this talk, I will present recent work in collaboration with Drivas, Shkoller and Vicol on the shock development problem for the 2D compressible Euler under azimuthal symmetry. The work represents the first full description of shock development; in particular, in addition to describing the shock front, we give the first detailed description of the phenomena of weak discontinuities conjectured by Landau and Lifschitz over half a century ago.