Publicação

Well-posedness for some perturbations of the kdv equation with low regularity data

Ver documento

Detalhes bibliográficos
Resumo: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 $\Phi(\xi)=-\xi^2$.
Autores principais:Carvajal, Xavier
Outros Autores:Panthee, Mahendra Prasad
Assunto:Bourgain spaces KdV equation Bourgain spaces local smoothing effect
Ano:2008
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso aberto
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

Registos relacionados

Atividades financiadas

Não foram encontrados projetos financiados.

Registos relacionados