Global well-posedness for dissipative Korteweg-de Vries equations

Stéphane Vento

This paper is devoted to the well-posedness for dissipative KdV equations $u_t+u_{xxx}+|D_x{|}^{2\alpha }u+u{u}_x=0$, $0<\alpha \le 1$. An optimal bilinear estimate is obtained in Bourgain's type…