John's blow up examples and scattering solutions for semi-linear wave equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913322237952000 |
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| author | Bernhardt, Louie Schlue, Volker Yu, Dongxiao |
| author_facet | Bernhardt, Louie Schlue, Volker Yu, Dongxiao |
| contents | In light of recent work of the third author, we revisit a classic example given by Fritz John of a semi-linear wave equation which exhibits finite in time blow up for all compactly supported data. We present the construction of future global solutions from asymptotic data given in arXiv:2204.12870(2022) for this specific example, and clarify the relation of this result of Yu to John's theorem. Furthermore we present a novel blow up result for finite energy solutions satisfying a sign condition due to the first author, and invoke this result to show that the constructed backwards in time solutions blow up in the past. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | John's blow up examples and scattering solutions for semi-linear wave equations Bernhardt, Louie Schlue, Volker Yu, Dongxiao Analysis of PDEs In light of recent work of the third author, we revisit a classic example given by Fritz John of a semi-linear wave equation which exhibits finite in time blow up for all compactly supported data. We present the construction of future global solutions from asymptotic data given in arXiv:2204.12870(2022) for this specific example, and clarify the relation of this result of Yu to John's theorem. Furthermore we present a novel blow up result for finite energy solutions satisfying a sign condition due to the first author, and invoke this result to show that the constructed backwards in time solutions blow up in the past. |
| title | John's blow up examples and scattering solutions for semi-linear wave equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.12878 |