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arXiv · 1803.01720

Pointwise convergence of Schr\"odinger solutions and multilinear refined Strichartz estimates

Xiumin Du·Larry Guth·Xiaochun Li·Ruixiang Zhang
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Abstract

We obtain partial improvement toward the pointwise convergence problem of Schr\"odinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geq 3$, $\lim_{t \to 0} e^{it\Delta}f(x) = f(x)$ almost everywhere with respect to Lebesgue measure for all $f \in H^s (\mathbb{R}^n)$ provided that $s>(n+1)/2(n+2)$. The proof uses linear refined Strichartz estimates. We also prove a multilinear refined Strichartz using decoupling and multilinear Kakeya.

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Xiumin Du, Larry Guth, Xiaochun Li, Ruixiang Zhang. 2018-03-02. Pointwise convergence of Schr\"odinger solutions and multilinear refined Strichartz estimates. https://arxiv.org/abs/1803.01720

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