Publicação
On KP-II type equations on cylinders
| Resumo: | In this article we study the generalized dispersion version of the Kadomtsev-Petviashvili II equation, on $\mathbb{T} \times \mathbb{R}$ and $\mathbb{T} \times \mathbb{R}^2$. We start by proving bilinear Strichartz type estimates, dependent only on the dimension of the domain but not on the dispersion. Their analogues in terms of Bourgain spaces are then used as the main tool for the proof of bilinear estimates of the nonlinear terms of the equation and consequently of local well-posedness for the Cauchy problem. |
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| Autores principais: | Grunrock, Axel |
| Outros Autores: | Panthee, Mahendra; Silva, Jorge Drumond |
| Assunto: | KP-II equation Local well-posedness Global well-posedness Space–time estimates |
| Ano: | 2009 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | In this article we study the generalized dispersion version of the Kadomtsev-Petviashvili II equation, on $\mathbb{T} \times \mathbb{R}$ and $\mathbb{T} \times \mathbb{R}^2$. We start by proving bilinear Strichartz type estimates, dependent only on the dimension of the domain but not on the dispersion. Their analogues in terms of Bourgain spaces are then used as the main tool for the proof of bilinear estimates of the nonlinear terms of the equation and consequently of local well-posedness for the Cauchy problem. |
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