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Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation

Terence Tao
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Abstract

The endpoint Strichartz estimates for the Schrödinger equation are 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.

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Terence Tao. 2004-10-20. Spherically averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equation. https://arxiv.org/abs/math/9811168

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