MR2829551 Stéphane VENTO Stéphane VENTO Global Well-Posedness for Dissipative Korteweg-de Vries Equations Funkcialaj Ekvacioj. Serio Internacia 54 2011 119--138 http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-1/54_119.pdf http://www.ams.org/mathscinet-getitem?mr=MR2829551 This paper is devoted to the well-posedness for dissipative KdV equations $u_t+u_{xxx}+|D_x|^{2\alpha}u+uu_x=0$, $0<\alpha\leq 1$. An optimal bilinear estimate is obtained in Bourgain's type spaces, which provides global well-posedness in $H^s({\bf R})$, $s>-3/4$ for $\alpha\leq1/2$ and $s>-3/(5-2\alpha)$ for $\alpha>1/2$. KdV-like equations, Bourgain spaces, Cauchy problem. 35Q53, 35A05, 35M10. 54-119 2011 Global Well-Posedness for Dissipative Korteweg-de Vries Equations Stéphane VENTO Stéphane VENTO
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