Beceanu, Marius; Chen, Gong Strichartz estimates for the Klein-Gordon equation in \(\mathbb{R}^{3+1}\). (English) Zbl 1515.81086 Pure Appl. Anal. 4, No. 4, 767-809 (2022). Summary: We prove standard and reversed Strichartz estimates for the Klein-Gordon equation in \(\mathbb{R}^{3+1}\). Instead of the Fourier theory, our analysis is based on fundamental solutions of the free equations and fractional integrations. We apply Strichartz estimates to study semilinear Klein-Gordon equations. Cited in 1 Document MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35B45 A priori estimates in context of PDEs Keywords:Klein-Gordon equation; Strichartz estimates; dispersive estimates PDFBibTeX XMLCite \textit{M. Beceanu} and \textit{G. Chen}, Pure Appl. Anal. 4, No. 4, 767--809 (2022; Zbl 1515.81086) Full Text: DOI arXiv References: [1] ; Agmon, Shmuel, Spectral properties of Schrödinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 2, 2, 151 (1975) · Zbl 0315.47007 [2] 10.1017/CBO9781107325937 · doi:10.1017/CBO9781107325937 [3] 10.1080/03605309408821056 · Zbl 0818.35054 · doi:10.1080/03605309408821056 [4] 10.1080/03605309308820977 · Zbl 0795.35059 · doi:10.1080/03605309308820977 [5] 10.2140/apde.2016.9.813 · Zbl 1353.35131 · doi:10.2140/apde.2016.9.813 [6] 10.1016/j.jfa.2013.11.010 · Zbl 1292.35063 · doi:10.1016/j.jfa.2013.11.010 [7] 10.1353/ajm.2020.0025 · Zbl 1445.35234 · doi:10.1353/ajm.2020.0025 [8] ; Bergh, Jöran; Löfström, Jörgen, Interpolation spaces : an introduction. Grundl. Math. Wissen., 223 (1976) · Zbl 0344.46071 [9] 10.1007/s00220-018-3170-4 · Zbl 1420.35287 · doi:10.1007/s00220-018-3170-4 [10] 10.1090/memo/1339 · Zbl 1484.35092 · doi:10.1090/memo/1339 [11] 10.1080/03605300701743749 · Zbl 1160.35363 · doi:10.1080/03605300701743749 [12] 10.1007/s00041-015-9428-8 · Zbl 1361.42011 · doi:10.1007/s00041-015-9428-8 [13] 10.2140/apde.2011.4.405 · Zbl 1270.35132 · doi:10.2140/apde.2011.4.405 [14] 10.1353/ajm.2020.0038 · Zbl 1465.35306 · doi:10.1353/ajm.2020.0038 [15] 10.1353/ajm.1998.0039 · Zbl 0922.35028 · doi:10.1353/ajm.1998.0039 [16] 10.1016/j.jfa.2004.07.005 · Zbl 1060.35025 · doi:10.1016/j.jfa.2004.07.005 [17] 10.4171/RMI/342 · Zbl 1041.35061 · doi:10.4171/RMI/342 [18] 10.4171/095 · Zbl 1235.37002 · doi:10.4171/095 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.