Quantization of Time-Like Energy for Wave Maps into Spheres
| Autor: | Roland Grinis |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Physics
Sequence Quantization (signal processing) 010102 general mathematics Mathematical analysis Boundary (topology) Statistical and Nonlinear Physics 35L70 Space (mathematics) 01 natural sciences Mathematics - Analysis of PDEs Singularity Cone (topology) Norm (mathematics) Light cone 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematical Physics Analysis of PDEs (math.AP) |
| Zdroj: | Communications in Mathematical Physics. 352:641-702 |
| ISSN: | 1432-0916 0010-3616 |
| Popis: | In this article we consider large energy wave maps in dimension 2+1, as in the resolution of the threshold conjecture by Sterbenz and Tataru, but more specifically into the unit Euclidean sphere, and study further the dynamics of the sequence of wave maps that are obtained by Sterbenz and Tataru after the final rescaling at a first, finite or infinite, time singularity. We prove that, on a suitably chosen sequence of time slices at this scaling, there is a decomposition of the map, up to an error with asymptotically vanishing energy, into a decoupled sum of rescaled solitons concentrating in the interior of the light cone and a term having asymptotically vanishing energy dispersion norm, concentrating on the null boundary and converging to a constant locally in the interior of the cone, in the energy space. Comment: 62 pages, some corrections and feedback implemented, Lemma 2.8 refined, comments welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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