Scattering for a mass critical NLS system below the ground state with and without mass-resonance condition

2018/10/18 by Inui, Takahisa, Kishimoto, Nobu, Nishimura, Kuranosuke · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.07904

Abstract

We consider a mass-critical system of nonlinear Schödinger equations \begincases i∂_t u +Δu =uv,
i∂_t v +κΔv =u², \endcases (t,x)∈ ℝ× ℝ⁴, where (u,v) is a ℂ²-valued unknown function and κ>0 is a constant. If κ=1/2, we say the equation satisfies mass-resonance condition. We are interested in the scattering problem of this equation under the condition M(u,v)

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