Multi-bubble solutions are constructed for the 4D energy-critical wave equation blowing up at N symmetric points with log(1/λ(t)) = (9c/4)^{1/3} t^{2/3} + O(t^{1/3}).
Kadar, Smooth finite time singularity formation without quantization, preprint, arXiv:2603.14985, 2026
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Construction of multi-bubble solutions for the energy-critical wave equation in dimension four
Multi-bubble solutions are constructed for the 4D energy-critical wave equation blowing up at N symmetric points with log(1/λ(t)) = (9c/4)^{1/3} t^{2/3} + O(t^{1/3}).