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

Wengu Chen, Junfeng Li, Changxing Miao

In this paper we consider some dissipative versions of the modified Korteweg de Vries equation $u_t+u_{xxx}+|D_x{|}^{\alpha }u+u^2{u}_x=0$ with $0<\alpha \le 3$. We prove some well-posedness result…