  We establish inhomogeneous Strichartz Estimates for the Schr{\"o}dinger
equation with singular and time dependent potentials for non-admissible pairs.
Our work extends the results provided by Vilela [23] and Foschi [6] where they
proved the results in the absence of potential. It also extends the works of
Pierfelice [20] and Burq, Planchon, Stalker, Tahvildar-Zadeh [3], who proved
the estimates for admissible pairs. We also extend the recent work of Mizutani,
Zhang, Zheng [17] and as an application of it, we improve the stability result
of Kenig-Merle [13], which in turn establishes a proof (alternative to [26]) of
existence of scattering solution for the energy critical focusing NLS with
inverse square potential.

Analysis of PDEs