Global well-posedness for dissipative Korteweg-de Vries equations

Stéphane Vento

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arXiv · 0706.1730

Global well-posedness for dissipative Korteweg-de Vries equations

Stéphane Vento

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Abstract

This paper is devoted to the well-posedness for dissipative KdV equations $u_t+u_{xxx}+|D_x|^{2α}u+uu_x=0$, $0<α\leq 1$. An optimal bilinear estimate is obtained in Bourgain's type spaces, which provides global well-posedness in $H^s(\R)$, $s>-3/4$ for $α\leq1/2$ and $s>-3/(5-2α)$ for $α>1/2$.

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BibTeX RIS

Stéphane Vento. 2007-06-12. Global well-posedness for dissipative Korteweg-de Vries equations. https://arxiv.org/abs/0706.1730

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