Local well-posedness and finite time blowup for fourth-order Schrödinger equation with complex coefficient

Xuan Liu, Ting Zhang

We consider the fourth-order Schrödinger equation $$i{\partial }_{t}u+{\Delta }^{2}u+\mu \Delta u+\lambda |u{|}^{\alpha }u=0,$$ where $\alpha >0,\mu =\pm 1$ or $0$ and $\lambda \in \mathbb{C}$. Firstly, we prove local well-posedness in…