Spherical Averaged Endpoint Strichartz Estimates for the Two-dimensional Schrodinger Equations with Inverse Square Potential

Abstract

In this dissertation, I investigate the two-dimensional Schrodinger equation with repulsive inverse square potential. I prove a version of the homogeneous endpoint Strichartz estimate, in which I replace the supremum norm on space by a norm that takes $L^2$ average in angular variable first and then supremum norm on radial variable.