Tzirakis, Nikolaos The Cauchy problem for the Klein-Gordon-Schrödinger system in low dimensions below the energy space. (English) Zbl 1075.35082 Commun. Partial Differ. Equations 30, No. 5-6, 605-641 (2005). The author deals with the Cauchy problem for the Klein-Gordon-Schrödinger equation in 1D, 2D and 3D cases. Existence of a global solution in the energy space is proved. Reviewer: Igor Andrianov (Köln) Cited in 8 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 42B35 Function spaces arising in harmonic analysis Keywords:global well-posedness; Klein-Gordon-Schrödinger equation; Cauchy problem; existence of a global solution PDFBibTeX XMLCite \textit{N. Tzirakis}, Commun. Partial Differ. Equations 30, No. 5--6, 605--641 (2005; Zbl 1075.35082) Full Text: DOI References: [1] Bachelot A., Ann. Inst. H. Poincaré, Analyse Non Linèaire 1 pp 453– (1984) [2] Baillon J. B., Contemporary Developments in Continuous Mechanics and PDEs pp 37– (1978) [3] Bourgain J., J. d’Analyse Math. 75 pp 267– (1998) · Zbl 0972.35141 · doi:10.1007/BF02788703 [4] Bourgain J., Intern. Mat. Res. Notices 5 pp 253– (1998) · Zbl 0917.35126 · doi:10.1155/S1073792898000191 [5] Colliander J., SIAM J. Math. Anal. 33 pp 649– (2001) · Zbl 1002.35113 · doi:10.1137/S0036141001384387 [6] Colliander J., SIAM J. Math. Anal. 34 pp 64– (2002) · Zbl 1034.35120 · doi:10.1137/S0036141001394541 [7] Colliander J., Math. Res. Lett. 9 pp 659– (2002) [8] Colliander J., J. Amer. Math. Soc. 16 pp 705– (2003) · Zbl 1025.35025 · doi:10.1090/S0894-0347-03-00421-1 [9] Colliander J., J. Funct. Anal. 21 pp 173– (2004) · Zbl 1062.35109 · doi:10.1016/S0022-1236(03)00218-0 [10] Ginibre J., J. Func. Anal. 151 pp 384– (1997) · Zbl 0894.35108 · doi:10.1006/jfan.1997.3148 [11] Komineas S., Physical Review E 65 pp 061905– (2002) · doi:10.1103/PhysRevE.65.061905 [12] Pecher H., Differential Integral Eq. 17 pp 179– (2004) 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.