Global existence and scattering for a class of nonlinear fourth-order Schrödinger equation below the energy space

Abstract

In this paper, we consider a class of nonlinear fourth-order Schrödinger equation,Using the I-method combined with the interaction Morawetz inequality, we establish the global well-posedness and scattering in H γ (R d ) with γ(d, ν) < γ < 2 for some value γ(d, ν) > 0.