Global dynamics below the ground state for the quadratic Schödinger system in 5d

Abstract

In this paper we consider the nonlinear Schrödinger system (NLS) with quadratic interaction in five dimensions. We determine the global behavior of the solutions to the system with data below the ground state. Our proof of the scattering result is based on an argument by Kenig Merle [16]. In particular, the new part of this paper is to deal with asymmetric interaction. A blowing up or growing up result is proved by combining the argument by Du Wu Zhang in [6] and a variational characterization of minimizers. Moreover, we show a blowing-up result if the data has finite variance or is radial.

References in corpus (1)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

Cited by in corpus (7)

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• Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrödinger system without mass-resonance
• Scattering for a mass critical NLS system below the ground state with and without mass-resonance condition
• Scattering For Mass-resonance Nonlinear Schrödinger System in 5D
• Scattering theory For Quadratic Nonlinear Schrödinger System in dimension six
• A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system