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Characterization of large energy solutions of the equivariant wave map problem. II. (English) Zbl 1315.35131

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.

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

Citations:

Zbl 1315.35130
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