Global wellposedness and scattering for the inhomogeneous fourth-order Schrodinger equation

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Fourth-order Schrödinger equations were proposed as a correction to the standard model for propagation of laser in nonlinear media and have since appeared in different contexts. In this talk, I will consider the inhomogeneous mass-critical fourth-order Schrödinger equation $iu_t+D^2u-Du+|u|^{8/n}u=0$ and prove global existence and scattering in $L^2$ in high dimensions. The main analysis is reduced to a good understanding of the scaling limit problems which are scale invariant. This is a joint work with Shuanglin Shao.