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Construction of a two bubbles blowing-up solution for the fourth order energy critical nonlinear Schrödinger equation (2304.14744v2)
Published 28 Apr 2023 in math.AP
Abstract: We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schr\"odinger equation in infinite time in dimension $N\geq 13$. 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 $|t|{-\frac{2}{N-12}}$. Moreover, the phase between the two bubbles form a right angle.