Jiaqi Liu, USC

Title: On self-similar converging shock waves

Abstract: The Guderley problem is a well-known hydrodynamic problem of a strong shock propagating radially in an ideal gas medium. The shock originates at infinity and collapses to a central point or an axis. In this talk, I will discuss the recent work on the rigorous proof of the construction of the Guderley solution. As a result, its solution is given in terms of similarity profiles as the Euler equations are transformed into a system of ordinary differential equations (ODEs). The proof is based on continuity arguments, nonlinear invariances, and barrier functions. This is joint work with Juhi Jang and Matthew Schrecker.