Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$
Herr S, Kwak B (2024)
Forum of Mathematics, Pi 12: e14.
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Autor*in
Herr, SebastianUniBi 
;
Kwak, Beomjong
;
Kwak, BeomjongEinrichtung
Abstract / Bemerkung
The optimal $L^4$-Strichartz estimate for the Schr{ö}dinger equation on $\mathbb{T}^2$ is proved, which improves an estimate of Bourgain. A new method based on incidence geometry is used. In addition, the approach yields a uniform $L^4$ bound on a logarithmic time scale, which implies global existence of solutions to the mass-critical NLS in $H^s(\mathbb{T}^2)$ for any $s>0$ and small data.
Erscheinungsjahr
2024
Zeitschriftentitel
Forum of Mathematics, Pi
Band
12
Art.-Nr.
e14
Page URI
https://pub.uni-bielefeld.de/record/2983170
Zitieren
Herr S, Kwak B. Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi. 2024;12: e14.
Herr, S., & Kwak, B. (2024). Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi, 12, e14. https://doi.org/10.1017/fmp.2024.11
Herr, Sebastian, and Kwak, Beomjong. 2024. “Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$”. Forum of Mathematics, Pi 12: e14.
Herr, S., and Kwak, B. (2024). Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi 12:e14.
Herr, S., & Kwak, B., 2024. Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi, 12: e14.
S. Herr and B. Kwak, “Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$”, Forum of Mathematics, Pi, vol. 12, 2024, : e14.
Herr, S., Kwak, B.: Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi. 12, : e14 (2024).
Herr, Sebastian, and Kwak, Beomjong. “Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$”. Forum of Mathematics, Pi 12 (2024): e14.
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