Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$
Herr S, Kwak B (Accepted)
Forum of Mathematics, Pi.
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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
2023
Zeitschriftentitel
Forum of Mathematics, Pi
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. Accepted.
Herr, S., & Kwak, B. (Accepted). Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi
Herr, Sebastian, and Kwak, Beomjong. Accepted. “Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$”. Forum of Mathematics, Pi.
Herr, S., and Kwak, B. (Accepted). Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi.
Herr, S., & Kwak, B., Accepted. Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi.
S. Herr and B. Kwak, “Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$”, Forum of Mathematics, Pi, Accepted.
Herr, S., Kwak, B.: Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$. Forum of Mathematics, Pi. (Accepted).
Herr, Sebastian, and Kwak, Beomjong. “Strichartz estimates and global well-posedness of the cubic NLS on $\mathbb{T}^{2}$”. Forum of Mathematics, Pi (Accepted).
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