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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.12380 |
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| _version_ | 1866917144831197184 |
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| author | Boiti, Chiara Manfrin, Renato |
| author_facet | Boiti, Chiara Manfrin, Renato |
| contents | We prove that the special Kirchhoff equation studied by Pokhozhaev admits a third-order conservation law. We further show that if the energy of the solution is sufficiently small, then the $L^2$-norms of the derivatives up to third order of the solution remain uniformly bounded with respect to time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A third-order conservation law for the Kirchhoff-Pokhozhaev equation Boiti, Chiara Manfrin, Renato Analysis of PDEs We prove that the special Kirchhoff equation studied by Pokhozhaev admits a third-order conservation law. We further show that if the energy of the solution is sufficiently small, then the $L^2$-norms of the derivatives up to third order of the solution remain uniformly bounded with respect to time. |
| title | A third-order conservation law for the Kirchhoff-Pokhozhaev equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.12380 |