| Abstract |
In critical PDEs, finite-time blow-up may occur while the scaling-critical norm remains bounded, with singularity formation arising from concentration and loss of compactness. In this first talk, we consider the radial focusing energy-critical wave equation in three dimensions and discuss the role of concentration-compactness and profile decomposition in the study of Type II blow-up. We then introduce radiation for the radial free wave equation and the channel of energy method. These ideas will provide the starting point for the rigidity analysis in the second talk.
[References]
1. H. Bahouri, P. Gérard, High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math. 121 (1999), 131–175.
2. C. E. Kenig, A. Lawrie, B. Liu, W. Schlag, Channels of energy for the linear radial wave equation, Adv. Math. 285 (2015), 877–936. |
