Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case

Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in $H^1({\mathbb{R}}^d)$ and then utilize the concentration-compactness method to show the global wellposedness and scattering versus blowup in $H^1({\mathbb{R}}^d)$ below the threshold for radial data when $d\le 4$.

40 pages, 0 figures

References in corpus (1)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case

Cited by in corpus (14)

• Orbital stability vs. scattering in the cubic-quintic Schrodinger equation
• Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs
• Normalized ground states for the NLS equation with combined nonlinearities
• Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case
• Sharp scattering threshold for the cubic-quintic NLS in the focusing-focusing regime
• On ground states for the 2D Schrodinger equation with combined nonlinearities and harmonic potential
• Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide ${\mathbb{R}}^2$ $\times$ ${\mathbb{T}}^2$
• Multiplicity of normalized solutions for a Schrödinger equation with critical growth in ${\mathbb{R}}^N$
• On scattering for the defocusing nonlinear Schrödinger equation on waveguide ${\mathbb{R}}^m$ $\times$ $\mathbb{T}$ (when $m=2,3$)
• Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations
• NLS equation with competing inhomogeneous nonlinearities: ground states, blow-up, and scattering
• On sharp scattering threshold for the mass-energy double critical NLS via double track profile decomposition
• On the two-power nonlinear Schrödinger equation with non-local terms in Sobolev-Lorentz spaces
• Scattering threshold for radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation in $d\ge 5$