2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172211In 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 pagesAnalysis of PDEs35Q53, 35A07text