Random data Cauchy theory for the fourth order nonlinear Schrödinger equation with cubic nonlinearity

Hiroyuki Hirayama, Mamoru Okamoto

We consider the Cauchy problem for the fourth order nonlinear Schrödinger equation with derivative nonlinearity $(i{\partial }_t+{\Delta }^2)u=\pm \partial (|u{|}^{2}u)$ on ${\mathbb{R}}^d$,…