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

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.

14 pages

References in corpus (6)

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• Strichartz Estimates in Spherical Coordinates
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Cited by in corpus (6)

• Numerical study of fractional Nonlinear Schrödinger equations
• Energy concentration of the focusing energy-critical FNLS
• Sharp Criteria of Scattering for the Fractional NLS
• Almost sure local wellposedness of energy critical fractional Schrödinger equations with hartree nonlinearity
• On the modified scattering of $3$-d Hartree type fractional Schrödinger equations with Coulomb potential
• Global existence for the nonlinear fractional Schrödinger equation with fractional dissipation