On the energy-critical fractional Schödinger equation in the radial case

2013/10/25 by Zihua Guo, Guo, Zihua, Yannick Sire +5
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1310.6816

openalex publication_date 2013/10/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for the energy-critical nonlinear Schrödinger equation with fractional Laplacian (fNLS) in the radial case. We obtain global well-posedness and scattering in the energy space in the defocusing case, and in the focusing case with energy below the ground state.

Citations

• On finite time blowup for mass-critical Hartree equations
• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
• Profile decompositions and Blowup phenomena of mass critical fractional Schrödinger equations
• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equation
• On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity

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• Scattering of solutions to nonlinear Schrödinger equations with regular potentials
• Global well-posedness, scattering and blow-up for the energy-critical, Schrödinger equation with general nonlinearity in the radial case