Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914327981719552 |
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| author | Trespalacios, Jessica |
| author_facet | Trespalacios, Jessica |
| contents | In this paper, we consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth global solutions inside the light cone. Finally, some applications are presented in the case of PCF solitons, a first step towards the study of its nonlinear stability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2201_02683 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons Trespalacios, Jessica Analysis of PDEs Mathematical Physics In this paper, we consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth global solutions inside the light cone. Finally, some applications are presented in the case of PCF solitons, a first step towards the study of its nonlinear stability. |
| title | Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2201.02683 |