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.
Shen, Nonexistence of multi-bubble radial solutions to the 3D energy critical wave equa- tion, preprint arXiv:2603.21602, 2026
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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.