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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2412.02131 |
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| _version_ | 1866917854474928128 |
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| author | Chen, Gong Lan, Yang Yuan, Xu |
| author_facet | Chen, Gong Lan, Yang Yuan, Xu |
| contents | For the 2D cubic (mass-critical) Zakharov-Kuznetsov equation, \begin{equation*} \partial_tϕ+\partial_{x_1}(Δϕ+ϕ^3)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}^{2}, \end{equation*} we prove that there exist no finite/infinite time blow-up solution with minimal mass in the energy space. This nonexistence result is in contrast to the one obtained by Martel-Merle-Raphaël [17] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. The proof relies on a refined ODE argument related to the modulation theory and a modified energy-virial Lyapunov functional with a monotonicity property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonexistence of minimal mass blow-up solution for the 2D cubic Zakharov-Kuznetsov equation Chen, Gong Lan, Yang Yuan, Xu Analysis of PDEs For the 2D cubic (mass-critical) Zakharov-Kuznetsov equation, \begin{equation*} \partial_tϕ+\partial_{x_1}(Δϕ+ϕ^3)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}^{2}, \end{equation*} we prove that there exist no finite/infinite time blow-up solution with minimal mass in the energy space. This nonexistence result is in contrast to the one obtained by Martel-Merle-Raphaël [17] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. The proof relies on a refined ODE argument related to the modulation theory and a modified energy-virial Lyapunov functional with a monotonicity property. |
| title | Nonexistence of minimal mass blow-up solution for the 2D cubic Zakharov-Kuznetsov equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.02131 |