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Global endpoint Strichartz estimates for Schrödinger equations on the cylinder \(\mathbb{R} \times \mathbb{T}\). (English) Zbl 1462.35345

Summary: We prove global in time Strichartz estimates on the semi-periodic cylinder with initial data in \(L^2\). This extends the local results of [H. Takaoka and N. Tzvetkov, J. Funct. Anal. 182, No. 2, 427–442 (2001; Zbl 0976.35085)] and the global estimates with loss of derivatives of [Z. Hani and the second author, Commun. Pure Appl. Math. 67, No. 9, 1466–1542 (2014; Zbl 1312.35159)] and the first author [“On global-in-time Strichartz estimates for the semiperiodic Schrödinger equation”, Preprint, arXiv:1901.01663].

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
28A50 Integration and disintegration of measures
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References:

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