Spherically averaged endpoint Strichartz estimates for the two-dimensional Schr'odinger equation

摘要

The endpoint Strichartz estimates for the Schr\"odinger equation are known tobe false in two dimensions. However, if one averages the solution in $L^2$ inthe angular variable, we show that the homogeneous endpoint and the retardedhalf-endpoint estimates hold, but the full retarded endpoint fails. Inparticular, the original versions of these estimates hold for radial data.