Côte, R.; Kenig, C. E.; Lawrie, A.; Schlag, W. Characterization of large energy solutions of the equivariant wave map problem. II. (English) Zbl 1315.35131 Am. J. Math. 137, No. 1, 209-250 (2015). This paper continues the study on wave maps started in the article: [the authors, ibid. 137, No. 1, 139–207 (2015; Zbl 1315.35130)]. The authors emphasize that both article have to be read together. The study on degree one solutions to the stated Cauchy problem is completed here with a result on the classification of such solutions having the energy below three times the energy of the harmonic map, given by the stereographic projection. Two scenarios are discussed: when the solution blows up in finite time and when the solution exists globally in time. Reviewer: Claudia Simionescu-Badea (Wien) Cited in 2 ReviewsCited in 29 Documents MSC: 35L71 Second-order semilinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations 35P25 Scattering theory for PDEs 47A40 Scattering theory of linear operators 35B44 Blow-up in context of PDEs Keywords:wave maps; energy solutions; harmonic map; scattering; stereographic projection Citations:Zbl 1315.35130 PDFBibTeX XMLCite \textit{R. Côte} et al., Am. J. Math. 137, No. 1, 209--250 (2015; Zbl 1315.35131) Full Text: DOI arXiv Link