Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D

Abstract

In this paper, we study the dynamics behavior of the (NLS system) with three waves interaction in the energy space $$H^1({\mathbb {R}}^5) \times H^1({\mathbb {R}}^5)\times H^1({\mathbb {R}}^5) $$ . Inspired by Dodson and Murphy (Math Res Lett 25(6):1805–1825, 2018), we establish an interaction Morawetz estimate for the (NLS system), together with the criterion which proved by Tao–Dodson–Murphy we can get the scattering under the ground state in energy space with mass-resonance. Under the radial assumption, we can remove the mass-resonance condition.