POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES

By Xiumin Du, Larry Guth, Xiaochun Li, Ruixiang Zhang. Forum of Mathematics, Sigma, 2018

72 citations recorded by the source corpus.

We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geqslant 3$ , $\lim _{t\rightarrow 0}e^{it\unicode[STIX]{x1D6E5}}f(x)$ $=f(x)$ 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/77a44a2a066d0699970e02ae44499b7a6367d4eb

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In Applied Mathematics

1. Ruixiang Zhang
2. Xiumin Du
3. Hong Wang
4. Yumeng Ou
5. Alex Iosevich
6. Larry Guth
7. Bochen Liu
8. Jean Bourgain

In Mathematical Physics

1. Ruixiang Zhang
2. Xiumin Du
3. Hong Wang
4. Yumeng Ou
5. Larry Guth
6. Alex Iosevich
7. Bochen Liu
8. Jean Bourgain

Citations in the corpus

• On Falconer’s distance set problem in the plane (2018, background): “2) which is related to the refined Strichartz estimates that appear in [5], [6], and [7].”
• Sharp L2 estimates of the Schrödinger maximal function in higher dimensions (2018, methodology): “In higher dimensions (n ≥ 3), Guth, Li and the authors [13] proved the convergence for s > n+1 2(n+2) .”