Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation

Abstract

We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension $N\ge 13$. 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.

Reference list updated. Final version, to appear in Nonlinearity