Threshold solutions for the energy-critical NLS system with quadratic interaction

2025/05/06 by Ardila, Alex H., Cely, Liliana, Meng, Fanfei · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.03124

Abstract

In this paper, we study the Cauchy problem for a quadratic nonlinear Schrödinger system in dimension six. In~\citeGaoMengXuZheng, the authors classified the behavior of solutions under the energy constraint E(u) < E(Q), where Q denotes the ground state. In this work, we classify the dynamics of radial solutions at the threshold energy E(u) = E(Q).

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• Dynamics of the Energy-Critical Nonlinear Schrödinger System in \mathbb R⁴

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