Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations

Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equation with double nonlinearities with opposite sign, with one term is mass-critical and the other term is mass-supercritical and energy-subcritical, which includes the famous two-dimensional cubic-quintic nonlinear Schrödinger equaton. We prove global wellposedness and scattering in $H^1({\mathbb{R}}^d)$ below the threshold for non-radial data when $1\le d\le 4$.

24 pages, comments are welcome. arXiv admin note: text overlap with arXiv:1401.2242

References in corpus (3)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Global well - posedness and scattering for the focusing, energy - critical nonlinear Schrödinger problem in dimension $d=4$ for initial data below a ground state threshold