Blow‐up dynamics of L²−critical inhomogeneous nonlinear Schrödinger equation

Abstract

The purpose of this work is to study the L 2 −critical focusing inhomogeneous nonlinear Schrödinger equationWe study the dynamical behavior for blow-up solutions when initial date ∈ H 1 (R N ) and satisfies || || 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 || || L 2 = ||Q|| L 2 . KEYWORDS blow-up, dynamical behavior, profile decomposition 9408

Blow‐up dynamics of L2−critical inhomogeneous fractional nonlinear Schrödinger equation

“…Motivated by the above discussion, in this paper, we investigate the L 2 concentration phenomenon of the problem . In Peng and Zhao, we investigated the L 2 concentration phenomenon for without the radial assumption and proved the main results by profile decomposition which equivalent to concentration‐compactness principle. But for , we can obtain the similar results by compact embedding theorem under the condition of radial assumption.…”

“…Recently, Farah and Guzman investigated the scattering for the radial focusing inhomogeneous nonlinear Schrödinger Equation by a profile decomposition and energy Pythagoream expansion in . More works of can be found in literature and the references therein. For problem , Saanouni studied the well‐posedness issues and stability of ground state by a sharp Gagliardo‐Nirenberg type inequality when b <0.…”