Dispersive decay for the mass-critical generalized Korteweg-de Vries equation and generalized Zakharov-Kuznetsov equations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912019082379264 |
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| author | Shan, Minjie |
| author_facet | Shan, Minjie |
| contents | In this paper, we discuss pointwise decay estimate for the solution to the mass-critical generalized Korteweg-de Vries (gKdV) equation with initial data $u_0\in H^{1/2}(\mathbb{R})$. It is showed that nonlinear solution enjoys the same decay rate as linear one. Moreover, we also quantify the decay for solutions to the generalized Zakharov-Kuznetsov equation which is a natural multi-dimensional extension of the gKdV equation. We obtain some decay estimates for nonlinear solutions to generalized Zakharov-Kuznetsov equations with small initial data in $H^2(\mathbb{R}^d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dispersive decay for the mass-critical generalized Korteweg-de Vries equation and generalized Zakharov-Kuznetsov equations Shan, Minjie Analysis of PDEs Primary 35Q53, Secondary 37L50 In this paper, we discuss pointwise decay estimate for the solution to the mass-critical generalized Korteweg-de Vries (gKdV) equation with initial data $u_0\in H^{1/2}(\mathbb{R})$. It is showed that nonlinear solution enjoys the same decay rate as linear one. Moreover, we also quantify the decay for solutions to the generalized Zakharov-Kuznetsov equation which is a natural multi-dimensional extension of the gKdV equation. We obtain some decay estimates for nonlinear solutions to generalized Zakharov-Kuznetsov equations with small initial data in $H^2(\mathbb{R}^d)$. |
| title | Dispersive decay for the mass-critical generalized Korteweg-de Vries equation and generalized Zakharov-Kuznetsov equations |
| topic | Analysis of PDEs Primary 35Q53, Secondary 37L50 |
| url | https://arxiv.org/abs/2409.05550 |