Vorticity in shock reflection problems and transport equations

In this talk we discuss self-similar solutions of two-dimensional Riemann problems with transonic shocks, focusing on regular shock reflection. After briefly reviewing known results for global self-similar solutions in the potential flow framework, we address the extension to the isentropic Euler system, where vorticity plays a central role. We show that regular reflection solutions exhibit low regularity and establish existence, uniqueness, and stability of renormalized solutions to the associated vorticity transport equation in this low-regularity setting. These results are obtained as a particular case of a more general analysis of transport equations without a time variable in domains of arbitrary dimension, allowing vector fields with possible stagnation points.