TY - UNPB

T1 - Construction of a two bubbles blowing-up solution for the fourth order energy critical nonlinear Schrödinger equation

AU - Holopainen, Ilkka

AU - Casteras, Jean-Baptiste

AU - Monsaingeon, Léonard

PY - 2023/4/28

Y1 - 2023/4/28

N2 - 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|−2N−12. Moreover, the phase between the two bubbles form a right angle.

AB - 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|−2N−12. Moreover, the phase between the two bubbles form a right angle.

KW - 111 Mathematics

KW - Nonlinear fourth-order Schrödinger equation, energy critical, two-bubble solution

U2 - 10.48550/arXiv.2304.14744

DO - 10.48550/arXiv.2304.14744

M3 - Preprint

BT - Construction of a two bubbles blowing-up solution for the fourth order energy critical nonlinear Schrödinger equation

ER -