Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909297216061440 |
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| author | Ban, Yingzhe Shan, Minjie |
| author_facet | Ban, Yingzhe Shan, Minjie |
| contents | We illustrate the dispersive blow up phenomena of the solutions of three dimensional generalized Zakharov-Kuznetsov equations. In particular, we construct smooth initial data such that, the associated global solutions fail to be $C^{1}$ at time $t$ in a null set containing all rational numbers, but are $C^{1}$ at all times $t$ which are generic irrational numbers. The key ingredient are to construct linear solutions which exhibit such phenomena and to prove nonlinear smoothing estimates for the full nonlinear model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations Ban, Yingzhe Shan, Minjie Analysis of PDEs 35Q53, 35B44 We illustrate the dispersive blow up phenomena of the solutions of three dimensional generalized Zakharov-Kuznetsov equations. In particular, we construct smooth initial data such that, the associated global solutions fail to be $C^{1}$ at time $t$ in a null set containing all rational numbers, but are $C^{1}$ at all times $t$ which are generic irrational numbers. The key ingredient are to construct linear solutions which exhibit such phenomena and to prove nonlinear smoothing estimates for the full nonlinear model. |
| title | Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations |
| topic | Analysis of PDEs 35Q53, 35B44 |
| url | https://arxiv.org/abs/2408.14737 |