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

Abstract

In this paper, we study the Cauchy problem for a quadratic nonlinear Schrödinger system in dimension six. In~\cite{GaoMengXuZheng}, 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 $E(u)=E(Q)$.

36 pages, comments are welcome!