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, Construction of multi-soliton solutions for the energy critical wave equation in dimension 3, preprint, arXiv:2409.05267, 2024
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Under the assumption of asymptotic multi-bubble decomposition with comparable scales, scaling parameters of 5D energy-critical wave solutions are of order t^{-2} and the modulation vector converges to a component of an algebraic set determined by the limiting bubble configuration.
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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}).
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Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five
Under the assumption of asymptotic multi-bubble decomposition with comparable scales, scaling parameters of 5D energy-critical wave solutions are of order t^{-2} and the modulation vector converges to a component of an algebraic set determined by the limiting bubble configuration.