The 3D energy-critical inhomogeneous nonlinear Schrodinger equation with strong singularity

In this paper, we study the Cauchy problem for the 3D energy-critical inhomogeneous nonlinear Schrödinger equation(INLS) $$i{\mathrm{\partial }}_{t}u+\mathrm{\Delta }u=\pm \mathrm{\mid }x{\mathrm{\mid }}^{-\alpha }\mathrm{\mid }u{\mathrm{\mid }}^{4-2\alpha }u$$ with strong singularity $3\mathrm{/}2\le \alpha <2$. The well-posedness problem is well-understood for $0<\alpha <3\mathrm{/}2$, but the case $3\mathrm{/}2\le \alpha <2$ has remained open so far. We address the local/small data global well-posedness result for $3\mathrm{/}2\le \alpha <11\mathrm{/}6$ by improving the inhomogeneous Strichartz estimates on the weighted space.