Bejenaru, Ioan Global results for Schrödinger maps in dimensions \(n\geq\) 3. (English) Zbl 1148.35083 Commun. Partial Differ. Equations 33, No. 3, 451-477 (2008). Author’s summary: We study the global well-posedness theory for the Schrödinger maps equation. We work in \(n + 1\) dimensions, for \(n\geq 3\), and prove a global well-posedness result for small initial data in \(\dot B _{2,1}^{\frac n 2}\). Reviewer: A. D. Osborne (Keele) Cited in 18 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 42B99 Harmonic analysis in several variables Keywords:Schrödinger maps; small data; well-posedness PDFBibTeX XMLCite \textit{I. Bejenaru}, Commun. Partial Differ. Equations 33, No. 3, 451--477 (2008; Zbl 1148.35083) Full Text: DOI arXiv References: [1] Bejenaru I., Adv. Math. 215 pp 263– (2007) · Zbl 1152.35049 [2] DOI: 10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R · Zbl 1028.35134 [3] Christ M., J. Funct. Anal. pp 179– (2001) [4] DOI: 10.1007/BF02877074 · Zbl 1019.53032 [5] DOI: 10.1007/BF02099195 · Zbl 0762.35008 [6] Ionescu D., Diff. Int. Equations 19 pp 1271– (2006) [7] DOI: 10.1090/S0894-0347-06-00551-0 · Zbl 1123.35055 [8] Ionescu D., Commun. Math. Phys. 271 pp 523– (2007) · Zbl 1137.35068 [9] Kato J., Math. Res. Lett. 12 pp 171– (2005) [10] DOI: 10.1088/0951-7715/18/5/007 · Zbl 1213.35358 [11] Koch H., Comm. Partial Differential Equations 32 pp 415– (2007) · Zbl 1387.35139 [12] DOI: 10.1080/03605300600856758 · Zbl 1122.35138 [13] DOI: 10.1002/cpa.10054 · Zbl 1028.58018 [14] DOI: 10.1002/cpa.20021 [15] Stein , E. M. ( 1993 ).Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton , NJ : Princeton University Press , pp. 347 – 349 . [16] Tao T., Commun. Math. Phys. 224 pp 443– (2001) · Zbl 1020.35046 [17] Tataru D., Comm. Partial Differential Equations 23 pp 1781– (1998) · Zbl 0914.35083 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.