Energy-critical NLS with quadratic potentials

Rowan Killip, Monica Visan, Xiaoyi Zhang

We consider the defocusing ${\dot{H}}^1$-critical nonlinear Schrödinger equation in all dimensions ($n\ge 3$) with a quadratic potential $V(x)=\pm \frac{1}{2}|x{|}^2$. We show global wel…