This analysis finds blowing-up solutions in the nonlinear Schrödinger equation, suggesting the presence of two bubbles in infinite time.
We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension N ⩾ 13 . Our solution is radially symmetric and converges asymptotically to the sum of two bubbles. The scale of one of the bubble is of order 1 whereas the other one is of order | t | − 2 N − 12 . Moreover, the phase between the two bubbles form a right angle.
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Castéras et al. (2025) studied this question.
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