Scattering theory For Quadratic Nonlinear Schrödinger System in dimension six

Abstract

In this paper, we study the solutions to the energy-critical quadratic nonlinear Schrödinger system in ${\dot{H}}^1\times {\dot{H}}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\mathrm{u}}_0$ is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of ${\mathrm{u}}_0$ is below or above that of the ground state.

34 pages

References in corpus (2)

• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Scattering for the quadratic nonlinear Schrödinger system in ${\mathbb{R}}^5$ without mass-resonance condition