Radial Similarity Flows for the Compressible Euler System

Abstract: The compressible Euler system provides the default model for inviscid gas flow. While routinely used in simulations, a proper mathematical understanding currently appears beyond reach. Radial similarity flows offer a rare instance where concrete flows can be studied in detail and we consider two cases: flows with focussing shocks and cavities. Due to their relevance for bomb-making and inertial confinement fusion, such solutions have been investigated extensively in the applied literature. They are of theoretical interest as they involve unbounded amplitudes (in velocity, pressure, temperature). We will outline the current mathematical understanding of these blowup solutions. [Based on joint work with Charis Tsikkou.]