We consider the blow-up results of the solution in W^2, 2 (RN) for the following quasilinear Schrödinger equation align* cases array{ll iuₜ+ u+2uh' (|u|²) h (|u|²) +uf (|u|²) =0, x RN, \\ u (x, 0) =u₀ (x), x RN, array } cases align* where h and f are real functions which related to various physical models. We prove that the W^2, 2 (RN) solutions must blow up if |x|u₀ L² (RN) (finite variance), and we give the upper bound of the blow-up time. We also show that without the finite variance assumption, the radial symmetric solutions in W^2, 2 (RN) must blow up in finite time for the whole class of initial data with strictly negative energy.
Guo et al. (Thu,) studied this question.