Hyperboloidal Foliations and Stability of Self-Similar Blowup in Nonlinear Wave Equations

Explore the mathematical analysis of singularity formation in nonlinear wave equations through this 24-minute conference lecture from the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the development of stability theory for wave evolution near self-similar solutions using hyperboloidal similarity coordinates, with particular focus on spacetime regions approaching the Cauchy horizon of singularities. Learn how hyperboloidal foliations provide a framework for understanding self-similar blowup phenomena in nonlinear wave equations, examining the mathematical tools and techniques used to analyze stability properties in these complex dynamical systems. Gain insights into advanced mathematical physics concepts including singularity theory, wave equation dynamics, and the geometric approach to studying solution behavior near critical points in spacetime.