On the blow-up scenario for some modified Serre-Green-Naghdi equations
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arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909127346749440 |
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| author | Guelmame, Billel |
| author_facet | Guelmame, Billel |
| contents | The present paper deals with a modified Serre-Green-Naghdi (mSGN) system that has been introduced by Clamond et al. to improve the dispersion relation. We present a precise blow-up scenario of the mSGN equations and we prove the existence of a class of solutions that develop singularities in finite time. All the presented results hold also for the Serre-Green-Naghdi system with weak surface tension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the blow-up scenario for some modified Serre-Green-Naghdi equations Guelmame, Billel Analysis of PDEs The present paper deals with a modified Serre-Green-Naghdi (mSGN) system that has been introduced by Clamond et al. to improve the dispersion relation. We present a precise blow-up scenario of the mSGN equations and we prove the existence of a class of solutions that develop singularities in finite time. All the presented results hold also for the Serre-Green-Naghdi system with weak surface tension. |
| title | On the blow-up scenario for some modified Serre-Green-Naghdi equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.02208 |