Spherically Averaged Endpoint Strichartz Estimates For The TwoDimensional Schrödinger Equation

Abstract

The endpoint Strichartz estimates for the Schrdinger equation is known to be false in two dimensions However, if one averages the solution in L 2 in the angular variable, we show that the homogeneous endpoint and the retarded half-endpoint estimates hold, but the full retarded endpoint fails. In particular, the original versions of these estimates hold for radial data.