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Global Well-posedness and Scattering for the Focusing Energy-critical Inhomogeneous Nonlinear Schr\"odinger Equation with Non-radial Data
We consider the focusing energy-critical inhomogeneous nonlinear Schr\"{o}dinger equation \[ iu_t + \Delta u = -|x|^{-b}|u|^{\alpha}u \] where $n \geq 3$, $0<b<\min(2, n/2)$, and $\alpha=(4-2b)/(n-2)$. We prove the global well-posedness and scattering for every $n \geq 3$, $0<b<\min(2, n/2)$, and every non-radial initial data $\phi \in \dot{H}^1(\mathbb{R}^n)$ by the concentration …