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

Wengu Chen·Junfeng Li·Changxing Miao
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Abstract

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.

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Wengu Chen, Junfeng Li, Changxing Miao. 2007-01-22. The well-posedness of Cauchy problem for dissipative modified Korteweg de Vries equations. https://arxiv.org/abs/math/0701602

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