On the energy-critical quadratic nonlinear Schrödinger system with three waves

2021/10/11 by Meng, Fanfei, Wang, Sheng, Xu, Chengbin · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.05277

Abstract

In this article, we consider the dynamics of the energy-critical quadratic nonlinear Schrödinger system \ \beginaligned amp; i u¹_t + κ₁ Δu¹ = -u²u³,
amp; i u²_t + κ₂ Δu² = -u¹u³,
amp; i u³_t + κ₃ Δu³ = -u¹u²,
\endaligned . (t, x) ∈ \R × \R⁶ in energy-space H¹ × H¹× H¹ , where the sign of potential energy can not be determined. We prove the scattering theory with mass-resonance (or with radial initial data) below ground state via concentration compactness method. We discover a family of new physically conserved quantities with mass-resonance which play an important role in the proof of scattering.

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