Preprint in the OpenAI Math release

Critical local smoothing for the three-dimensional wave equation

OpenAI

Abstract

We prove the critical L $^{3}$ local smoothing estimate for the wave equation in three spatial dimensions, with every positive Sobolev loss. This resolves Sogge's Euclidean local smoothing conjecture in dimension three.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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