079. Local smoothing in three dimensions

Local smoothing in three dimensions

1 paper

Resolves Sogge's local smoothing conjecture for the Euclidean wave equation in three spatial dimensions. The estimate holds throughout the full strict range \(2\lt p\lt \infty\), with Sobolev regularity above \(\max\{0,1-3/p\}\). In particular, the critical L³ estimate holds with every positive Sobolev loss.

Papers 1

Critical local smoothing for the three-dimensional wave equation

OpenAI · September 24, 2026

We prove the critical L³ 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.

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@misc{OAI:Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026,
  author = {{OpenAI}},
  title = {{Critical local smoothing for the three-dimensional wave equation}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026/paper.pdf}{OAI:Critical-local-smoothing-for-the-three-dimensional-wave-equation-September-24-2026}},
  year = {2026}
}

Local smoothing in three dimensions

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Papers 1

Critical local smoothing for the three-dimensional wave equation

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