Dating back to Guderley’s pioneering work in 1942, the Guderley problem is a classical problem in compressible fluid dynamics describing the implosion and subsequent reflection of a strong spherical shock wave. An initially converging shock propagates toward the origin, strengthens as it collapses, and eventually develops a singularity. After the collapse, an outgoing shock emerges and propagates outward.

In this talk, I will present our rigorous construction of self-similar converging and diverging shock solutions for the adiabatic exponent $\gamma\in(1,3]$. These solutions are analytic away from the shock interfaces and the blow-up point. The proof relies on continuity arguments, nonlinear invariances, and barrier functions.