The well-posedness of Cauchy problem for dissipative modified Korteweg de Vries equations

Chen, Wengu; Li, Junfeng; Miao, Changxing

The well-posedness of Cauchy problem for dissipative modified Korteweg de Vries equations

Authors

Chen, Wengu

Li, Junfeng

Miao, Changxing

Description

In this paper we consider some dissipative versions of the modified Korteweg de Vries equation $u_t+u_{xxx}+|D_x|^αu+u^2u_x=0$ with $0<α\leq 3$. We prove some well-posedness results on the associated Cauchy problem in the Sobolev spaces $H^s({\Bbb R})$ for $s>1/4-α/4$ on the basis of the $[k; Z]-$multiplier norm estimate obtained by Tao in \cite{Tao} for KdV equation.
20 pages