For the half-wave evolution in three spatial dimensions, the spacetime L3 norm on times [1,2] is bounded by the input L3 Sobolev norm with every positive derivative loss epsilon.
For the half-wave evolution in three spatial dimensions, the spacetime L3 norm on times [1,2] is bounded by the input L3 Sobolev norm with every positive derivative loss epsilon. The estimate yields the conjectured strict Euclidean local-smoothing range for all 2 < p < infinity.
For the half-wave evolution in three spatial dimensions, the spacetime L3 norm on times [1,2] is bounded by the input L3 Sobolev norm with every positive derivative loss epsilon. The estimate yields the conjectured strict Euclidean local-smoothing range for all 2 < p < infinity.
If correct, resolves Sogge’s Euclidean local-smoothing conjecture in three spatial dimensions.
Does time averaging give the conjectured local-smoothing gain for waves in three dimensions?
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OpenAI reports critical three-dimensional wave local smoothing
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