Blow‐up dynamics of L2−critical inhomogeneous nonlinear Schrödinger equation. (4th October 2018) - Peng, Congming; Zhao, Dun
Abstract : The purpose of this work is to study the L 2 −critical focusing inhomogeneous nonlinear Schrödinger equation i ∂ t u = − Δ u − | x | − b | u | 4 − 2 b N u, ( t, x ) ∈ R × R N, with 0 < b < 1. We study the dynamical behavior for blow‐up solutions when initial date ϕ ∈ H 1 ( R N ) and satisfies ‖ ϕ ‖ L 2 ≥ ‖ Q ‖ L 2, where Q is the ground state solution of our problem. Furthermore, we obtain the determination of the blow‐up solutions when ‖ ϕ ‖ L 2 = ‖ Q ‖ L 2 .