Blow‐up dynamics of L2−critical inhomogeneous fractional nonlinear Schrödinger equation. (16th July 2019)

• Record Type: Journal Article
• Authors: Peng, Congming; Zhang, Ying; Ma, Caochuan
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 18(2020)
• Page Start: 6896
• Page End: 6905
• Publication Date: 2019-07-16
• Subjects: blow up -- compact lemma -- dynamical behavior; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5795
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The purpose of this work is to investigate the blow‐up dynamics of L 2 −critical focusing inhomogeneous fractional nonlinear Schrödinger equation: i ∂ t u − ( − Δ ) s u + | x | − b | u | 2 σ u = 0, ( t, x ) ∈ R × R N, with 0< b <1. For this, we establish a new compactness lemma related to the equation. By applying this lemma, we study the dynamical behavior for blow‐up solutions for initial data φ ∈ H s ( R N ) satisfying ‖ φ ‖ L 2 ≥ ‖ Q ‖ L 2, where Q is the ground state solution of our problem.