Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/11583
Título: | Well-posedness for some perturbations of the kdv equation with low regularity data |
Autor(es): | Carvajal, Xavier Panthee, Mahendra Prasad |
Palavras-chave: | Bourgain spaces KdV equation Bourgain spaces local smoothing effect |
Data: | 2008 |
Editora: | Texas State University. Department of Mathematics |
Revista: | Electronic Journal of Differential Equations |
Citação: | "Electronic Journal of Differential Equations". ISSN 1072-6691. 2 (2008) 1-18. |
Resumo(s): | We study some well-posedness issues of the initial value problem associated with the equation $$ u_t+u_{xxx}+\eta Lu+uu_x=0, \quad x \in \mathbb{R}, \; t\geq 0, $$ where $\eta>0$, $\widehat{Lu}(\xi)=-\Phi(\xi)\hat{u}(\xi)$ and $\Phi \in \mathbb{R}$ is bounded above. Using the theory developed by Bourgain and Kenig, Ponce and Vega, we prove that the initial value problem is locally well-posed for given data in Sobolev spaces $H^s(\mathbb{R})$ with regularity below $L^2$. Examples of this model are the Ostrovsky-Stepanyams-Tsimring equation for $\Phi(\xi)=|\xi|-|\xi|^3$, the derivative Korteweg-de Vries-Kuramoto-Sivashinsky equation for $\Phi(\xi)=\xi^2-\xi^4$, and the Korteweg-de Vries-Burguers equation for $\Phi(\xi)=-\xi^2$. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/11583 |
ISSN: | 1072-6691 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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KdV-Pert.pdf | 257,57 kB | Adobe PDF | Ver/Abrir |