Dynamics of the non-radial energy-critical inhomogeneous NLS
Dynamics of the non-radial energy-critical inhomogeneous NLS
We consider the focusing inhomogeneous nonlinear Schr\"odinger equation \[ i\partial_t u + \Delta u + |x|^{-b}|u|^\alpha u = 0\qtq{on}\R\times\R^N, \] with $\alpha=\tfrac{4-2b}{N-2}$, $N=\{3,4,5\}$ and $0<b\leq \min\Big\{\tfrac{6-N}{2},\tfrac{4}{N}$\Big\}. This paper establishes global well-posedness and scattering for the non-radial energy-critical case in $\dot{H}^1(\R^N)$. It extends the previous research by Murphy and the first …