Here we study finite-time blow-up solutions of two-component system of nonlinear
Schr¨odinger equations with a time-dependent nonlinearity. From main
theorem in this paper, the system may have a solution (Φ,Ψ) such that both
∥▽Φ∥L2(Ω) and ∥▽Ψ∥L2(Ω) blow up at the same time but we don’t know whether ∥Φ∥L∞(Ω) and ∥Ψ∥L∞(Ω) blow up simultaneously.
