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A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system

  • * Corresponding author: Masaru Hamano

    * Corresponding author: Masaru Hamano 

The first author is supported by JSPS KAKENHI Grant Number JP19J13300

The second author is supported by JSPS KAKENHI Grant Numbers JP17K14219, JP17H02854, JP17H02851, and JP18KK0386

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  • In this paper, we consider the quadratic nonlinear Schrödinger system in three space dimensions. Our aim is to obtain sharp scattering criteria. Because of the mass-subcritical nature, it is difficult to do so in terms of conserved quantities. The corresponding single equation is studied by the second author and a sharp scattering criterion is established by introducing a distance from a trivial scattering solution, the zero solution. By the structure of the nonlinearity we are dealing with, the system admits a scattering solution which is a pair of the zero function and a linear Schrödinger flow. Taking this fact into account, we introduce a new optimizing quantity and give a sharp scattering criterion in terms of it.

    Mathematics Subject Classification: Primary: 35Q55.


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