Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schr\"odinger equation

We consider the inhomogeneous nonlinear Schr"odinger equation (INLS) in ${\mathbb{R}}^N$, $N\ge 1$, $$i{\mathrm{\partial }}_{t}u+\mathrm{\Delta }u+\mathrm{\mid }x{\mathrm{\mid }}^{-b}\mathrm{\mid }u{\mathrm{\mid }}^{p-1}u=0,$$ with finite-variance initial data $u_0\in H^1({\mathbb{R}}^N)$. We extend the dichotomy between scattering and blow-up for solutions above the mass-energy threshold (and with arbitrarily large energy). We also show other two blow-up criteria, wich are valid in any mass-supercritical setting, given there is local well-posedness.