2 problems

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The local Schrödinger smoothing conjecture in Euclidean space
Consider the free Schrödinger evolution on $\mathbb{R}^n$ , given by … For $1<p<\infty$ , let $W^{\alpha,p}(\mathbb{R}^n)$ denote the Sobolev space. Euclidean Schrödinger smoothing c…
Conjectureopenharmonic-analysis schrodinger-equations smoothing-estimatesarXiv posted 2 days ago
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Sugimoto–Ruzhansky invariant smoothing estimate for non-dispersive equations
Let $L=\partial_t+ia(t,D_x)$ be an operator, where $a(t,D_x)$ is the spatial pseudodifferential operator appearing in the evolution, and let $s$ and $C$ be as in the estimate. The…
Conjectureopennon-dispersive-equations partial-differential-equations smoothing-estimatesarXiv posted 2 days ago

The local Schrödinger smoothing conjecture in Euclidean space