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Delve into the third lecture of a four-part graduate-level series on super critical singularities in non-linear partial differential equations. Explore the concept of self-similar solutions for compressible Euler equations, a crucial aspect in understanding singularity formation in fluid mechanics. Gain insights into the recent discoveries of new mechanisms in defocusing problems and their profound connections to fluid dynamics. Learn about the key results, open problems, and essential proof steps in this field. This comprehensive lecture, delivered by Pierre Raphaël from the University of Cambridge, offers a deep dive into the mathematical foundations of singularity formation, building upon the classical problem's physical roots and recent advancements in understanding bubbling phenomena for focusing problems.
